?      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~             ! ! ! ! """"""""""""""""""# #!#"###$#%#&#'#(#)#*#+#,#-$.$/$0$1$2$3$4$5$6$789:;<=>?@ABCDEFGHIJKLMNOPQRS%T%U%V%W%X%Y%Z%[%\%]%^%_%`%a&b&c&d&e&f&g&h&i&j&k&l&m'n(o(p(q(r(s(t(u)v)w)x)y)z){)|)})~*****************************++++++++++++++++++++++++++++++++++++++++++++,,,,,,,--..........9/portable (uses FFI) provisionalAlberto Ruiz <aruiz@um.es>1description of GSL error codes clear the fpu debug x = trace (show x) xuseful for expressions like sortBy (compare `on` length) partit 3 [1..9] == [[1,2,3],[4,5,6],[7,8,9]]1obtains the common value of a property of a list postfix function application (flip ($)) specialized fromIntegral Aerror codes for the auxiliary functions required by the wrappers check the error code 410portable (uses FFI) provisionalAlberto Ruiz <aruiz@um.es>HA one-dimensional array of objects stored in a contiguous memory block.  number of elements  $foreign pointer to the memory block  creates a Vector from a list: > fromList [2,3,5,7] 4 |> [2.0,3.0,5.0,7.0] 'extracts the Vector elements to a list > toList (linspace 5 (1,10)) [1.0,3.25,5.5,7.75,10.0] An alternative to  $ with explicit dimension. The input F list is explicitly truncated if it is too long, so it may safely 1 be used, for instance, with infinite lists. >This is the format used in the instances for Show (Vector a).  1access to Vector elements without range checking  /access to Vector elements with range checking. 5takes a number of consecutive elements from a Vector  > subVector 2 3 (fromList [1..10]) 3 |> [3.0,4.0,5.0]index of the starting element number of elements to extract source result Reads a vector position: > fromList [0..9] @> 7 7.02creates a new Vector by joining a list of Vectors > join [fromList [1..5], constant 1 3] %8 |> [1.0,2.0,3.0,4.0,5.0,1.0,1.0,1.0]Ztransforms a complex vector into a real vector with alternating real and imaginary parts Ytransforms a real vector into a complex vector with alternating real and imaginary parts map on Vectors zipWith for Vectors               1portable (uses FFI) provisionalAlberto Ruiz <aruiz@um.es>-Auxiliary class. (r0,c0) starting position  (rt,ct) dimensions of submatrix @Matrix representation suitable for GSL and LAPACK computations.  Matrix transpose.  !"*Creates a vector by concatenation of rows > flatten (ident 3) )9 |> [1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0]#the inverse of Data.Packed.Matrix.fromLists $(creates a Matrix from a list of vectors %3extracts the rows of a matrix as a list of vectors &4Creates a matrix from a list of vectors, as columns '7Creates a list of vectors from the columns of a matrix (Reads a matrix position. )*Creates a matrix from a vector by grouping the elements in rows with the desired number of columns. (GNU-Octave groups by columns. To do it you can define reshapeF r = trans . reshape r (where r is the desired number of rows.) > reshape 4 (  [1..12]) (3><4)  [ 1.0, 2.0, 3.0, 4.0  , 5.0, 6.0, 7.0, 8.0  , 9.0, 10.0, 11.0, 12.0 ]+Bapplication of a vector function on the flattened matrix elements ,Dapplication of a vector function on the flattened matrices elements !"#$-$Extracts a submatrix from a matrix. (r0,c0) starting position  (rt,ct) dimensions of submatrix  input matrix result %2obtains the complex conjugate of a complex vector &Dcreates a complex vector from vectors with real and imaginary parts 'the inverse of & .]loads a matrix from an ASCII file (the number of rows and columns must be known in advance). 7 ( !)"#$%&'(*+)*,+,!"-./#$-01%&'.-   !"#$%&'()*+,!"#$-%&'.portable (uses FFI) provisionalAlberto Ruiz <aruiz@um.es>52345678/0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVVobtains different functions of a vector: norm1, norm2, max, min, posmax, posmin, etc. W(map of real vectors with given function X+map of complex vectors with given function Y(map of real vectors with given function Z+map of complex vectors with given function [&elementwise operation on real vectors \)elementwise operation on complex vectors ./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\./543210VDUTSRQPONMLKJIHGFEWX=CBA@?>YZ6<;:987[\./5432100123456<;:987789:;<=CBA@?>>?@ABCDUTSRQPONMLKJIHGFEEFGHIJKLMNOPQRSTUVWXYZ[\2portable provisionalAlberto Ruiz <aruiz@um.es>       ( !)"#$%&'(*+)*,+,!"-./#$-01%&'.portable provisionalAlberto Ruiz <aruiz@um.es>"]9^:;<_`abcdefghijk=>lmnopqrstuvwx]^_`abcdefghijklmnopqrstuvwx^k_fahide]xltnuvqrjbc`gwopms]^_`abcdefghijklmnopqrstuvwxuses ffi provisional!Alberto Ruiz (aruiz at um dot es)?Vconversion of Haskell functions into function pointers that can be used in the C side @A'type: 0 central, 1 forward, 2 backward initial step size  function $point where the derivative is taken result and error y'Adaptive central difference algorithm, gsl_deriv_central. For example: " > let deriv = derivCentral 0.01  > deriv sin (pi/4) ,(0.7071067812000676,1.0600063101654055e-10)  > cos (pi/4) 0.7071067811865476 initial step size  function $point where the derivative is taken result and absolute error z'Adaptive forward difference algorithm, gsl_deriv_forwardX. The function is evaluated only at points greater than x, and never at x itself. The derivative is returned in result and an estimate of its absolute error is returned in abserr. This function should be used if f(x) has a discontinuity at x, or is undefined for values less than x. A backward derivative can be obtained using a negative step. initial step size  function $point where the derivative is taken result and absolute error {(Adaptive backward difference algorithm, gsl_deriv_backward. initial step size  function $point where the derivative is taken result and absolute error yz{yz{yz{uses ffi provisional!Alberto Ruiz (aruiz at um dot es)BCDVconversion of Haskell functions into function pointers that can be used in the C side |Numerical integration using gsl_integration_qags9 (adaptive integration with singularities). For example: >% let quad = integrateQAGS 1E-9 1000 ># let f a x = x**(-0.5) * log (a*x) > quad (f 1) 0 1 *(-3.999999999999974,4.871658632055187e-13)precision (e.g. 1E-9) (size of auxiliary workspace (e.g. 1000) 0function to be integrated on the interval (a,b) a b $result of the integration and error }Numerical integration using gsl_integration_qngA (useful for fast integration of smooth functions). For example: > let quad = integrateQNG 1E-6 > quad (\x -> 4/(1+x*x)) 0 1 )(3.141592653589793,3.487868498008632e-14)precision (e.g. 1E-9) 0function to be integrated on the interval (a,b) a b $result of the integration and error |}}||}uses ffi provisional!Alberto Ruiz (aruiz at um dot es)E~Fast 1D Fourier transform of a  (F G) using gsl_fft_complex_forward6. It uses the same scaling conventions as GNU Octave. > fft (  [1,2,3,4]) Dvector (4) [10.0 :+ 0.0,(-2.0) :+ 2.0,(-2.0) :+ 0.0,(-2.0) :+ (-2.0)]The inverse of ~, using gsl_fft_complex_inverse. ~~~ uses ffi provisional!Alberto Ruiz (aruiz at um dot es)H0Solution of general polynomial equations, using gsl_poly_complex_solve. For example, ( the three solutions of x^3 + 8 = 0 > polySolve [8,0,0,1] [(-1.9999999999999998) :+ 0.0,  1.0 :+ 1.732050807568877,  1.0 :+ (-1.732050807568877)]@The example in the GSL manual: To find the roots of x^5 -1 = 0: > polySolve [-1, 0, 0, 0, 0, 1] .[(-0.8090169943749475) :+ 0.5877852522924731, 0(-0.8090169943749475) :+ (-0.5877852522924731), +0.30901699437494734 :+ 0.9510565162951536, .0.30901699437494734 :+ (-0.9510565162951536),  1.0 :+ 0.0]I3JKLVconversion of Haskell functions into function pointers that can be used in the C side MNOJKLMNOPQJKLMNO4uses ffi provisional!Alberto Ruiz (aruiz at um dot es) RSTUVWXYaccess to a sf_result Zaccess to sf_result_e10 VWXYZ VWXYZ uses ffi provisional!Alberto Ruiz (aruiz at um dot es)0[\]^_`abcdefghijklmnopqrRwrapper for int gsl_sf_airy_Ai_e(double x,gsl_mode_t mode,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_airy_Ai_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky =wrapper for double gsl_sf_airy_Ai(double x,gsl_mode_t mode);  fhttp://www.google.com/search?q=gsl_sf_airy_Ai&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Rwrapper for int gsl_sf_airy_Bi_e(double x,gsl_mode_t mode,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_airy_Bi_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky =wrapper for double gsl_sf_airy_Bi(double x,gsl_mode_t mode);  fhttp://www.google.com/search?q=gsl_sf_airy_Bi&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for int gsl_sf_airy_Ai_scaled_e(double x,gsl_mode_t mode,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_airy_Ai_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for double gsl_sf_airy_Ai_scaled(double x,gsl_mode_t mode);  mhttp://www.google.com/search?q=gsl_sf_airy_Ai_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for int gsl_sf_airy_Bi_scaled_e(double x,gsl_mode_t mode,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_airy_Bi_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for double gsl_sf_airy_Bi_scaled(double x,gsl_mode_t mode);  mhttp://www.google.com/search?q=gsl_sf_airy_Bi_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Xwrapper for int gsl_sf_airy_Ai_deriv_e(double x,gsl_mode_t mode,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_airy_Ai_deriv_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Cwrapper for double gsl_sf_airy_Ai_deriv(double x,gsl_mode_t mode);  lhttp://www.google.com/search?q=gsl_sf_airy_Ai_deriv&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Xwrapper for int gsl_sf_airy_Bi_deriv_e(double x,gsl_mode_t mode,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_airy_Bi_deriv_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Cwrapper for double gsl_sf_airy_Bi_deriv(double x,gsl_mode_t mode);  lhttp://www.google.com/search?q=gsl_sf_airy_Bi_deriv&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky _wrapper for int gsl_sf_airy_Ai_deriv_scaled_e(double x,gsl_mode_t mode,gsl_sf_result* result);  uhttp://www.google.com/search?q=gsl_sf_airy_Ai_deriv_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for double gsl_sf_airy_Ai_deriv_scaled(double x,gsl_mode_t mode);  shttp://www.google.com/search?q=gsl_sf_airy_Ai_deriv_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky _wrapper for int gsl_sf_airy_Bi_deriv_scaled_e(double x,gsl_mode_t mode,gsl_sf_result* result);  uhttp://www.google.com/search?q=gsl_sf_airy_Bi_deriv_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for double gsl_sf_airy_Bi_deriv_scaled(double x,gsl_mode_t mode);  shttp://www.google.com/search?q=gsl_sf_airy_Bi_deriv_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_airy_zero_Ai_e(int s,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_airy_zero_Ai_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_airy_zero_Ai(int s);  khttp://www.google.com/search?q=gsl_sf_airy_zero_Ai&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_airy_zero_Bi_e(int s,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_airy_zero_Bi_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_airy_zero_Bi(int s);  khttp://www.google.com/search?q=gsl_sf_airy_zero_Bi&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_airy_zero_Ai_deriv_e(int s,gsl_sf_result* result);  shttp://www.google.com/search?q=gsl_sf_airy_zero_Ai_deriv_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_airy_zero_Ai_deriv(int s);  qhttp://www.google.com/search?q=gsl_sf_airy_zero_Ai_deriv&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_airy_zero_Bi_deriv_e(int s,gsl_sf_result* result);  shttp://www.google.com/search?q=gsl_sf_airy_zero_Bi_deriv_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_airy_zero_Bi_deriv(int s);  qhttp://www.google.com/search?q=gsl_sf_airy_zero_Bi_deriv&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  uses ffi provisional!Alberto Ruiz (aruiz at um dot es)stuvwxyz{|}~Dwrapper for int gsl_sf_bessel_J0_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_J0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_J0(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_J0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_J1_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_J1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_J1(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_J1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_bessel_Jn_e(int n,double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_Jn_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_bessel_Jn(int n,double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_Jn&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for int gsl_sf_bessel_Jn_array(int nmin,int nmax,double x,double* result_array);  nhttp://www.google.com/search?q=gsl_sf_bessel_Jn_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_Y0_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_Y0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_Y0(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_Y0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_Y1_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_Y1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_Y1(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_Y1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_bessel_Yn_e(int n,double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_Yn_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_bessel_Yn(int n,double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_Yn&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for int gsl_sf_bessel_Yn_array(int nmin,int nmax,double x,double* result_array);  nhttp://www.google.com/search?q=gsl_sf_bessel_Yn_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_I0_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_I0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_I0(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_I0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_I1_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_I1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_I1(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_I1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_bessel_In_e(int n,double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_In_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_bessel_In(int n,double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_In&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for int gsl_sf_bessel_In_array(int nmin,int nmax,double x,double* result_array);  nhttp://www.google.com/search?q=gsl_sf_bessel_In_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_I0_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_I0_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_I0_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_I0_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_I1_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_I1_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_I1_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_I1_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Qwrapper for int gsl_sf_bessel_In_scaled_e(int n,double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_In_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for double gsl_sf_bessel_In_scaled(int n,double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_In_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky `wrapper for int gsl_sf_bessel_In_scaled_array(int nmin,int nmax,double x,double* result_array);  uhttp://www.google.com/search?q=gsl_sf_bessel_In_scaled_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_K0_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_K0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_K0(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_K0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_K1_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_K1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_K1(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_K1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_bessel_Kn_e(int n,double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_Kn_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_bessel_Kn(int n,double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_Kn&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for int gsl_sf_bessel_Kn_array(int nmin,int nmax,double x,double* result_array);  nhttp://www.google.com/search?q=gsl_sf_bessel_Kn_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_K0_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_K0_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_K0_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_K0_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_K1_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_K1_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_K1_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_K1_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Qwrapper for int gsl_sf_bessel_Kn_scaled_e(int n,double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_Kn_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for double gsl_sf_bessel_Kn_scaled(int n,double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_Kn_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky `wrapper for int gsl_sf_bessel_Kn_scaled_array(int nmin,int nmax,double x,double* result_array);  uhttp://www.google.com/search?q=gsl_sf_bessel_Kn_scaled_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_j0_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_j0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_j0(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_j0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_j1_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_j1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_j1(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_j1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_j2_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_j2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_j2(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_j2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_bessel_jl_e(int l,double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_jl_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_bessel_jl(int l,double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_jl&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Pwrapper for int gsl_sf_bessel_jl_array(int lmax,double x,double* result_array);  nhttp://www.google.com/search?q=gsl_sf_bessel_jl_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Twrapper for int gsl_sf_bessel_jl_steed_array(int lmax,double x,double* jl_x_array);  thttp://www.google.com/search?q=gsl_sf_bessel_jl_steed_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_y0_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_y0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_y0(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_y0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_y1_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_y1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_y1(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_y1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_bessel_y2_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_y2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_bessel_y2(double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_y2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_bessel_yl_e(int l,double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_bessel_yl_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_bessel_yl(int l,double x);  hhttp://www.google.com/search?q=gsl_sf_bessel_yl&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Pwrapper for int gsl_sf_bessel_yl_array(int lmax,double x,double* result_array);  nhttp://www.google.com/search?q=gsl_sf_bessel_yl_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_i0_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_i0_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_i0_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_i0_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_i1_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_i1_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_i1_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_i1_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_i2_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_i2_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_i2_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_i2_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Qwrapper for int gsl_sf_bessel_il_scaled_e(int l,double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_il_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for double gsl_sf_bessel_il_scaled(int l,double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_il_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Wwrapper for int gsl_sf_bessel_il_scaled_array(int lmax,double x,double* result_array);  uhttp://www.google.com/search?q=gsl_sf_bessel_il_scaled_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_k0_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_k0_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_k0_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_k0_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_k1_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_k1_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_k1_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_k1_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for int gsl_sf_bessel_k2_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_k2_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6wrapper for double gsl_sf_bessel_k2_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_k2_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Qwrapper for int gsl_sf_bessel_kl_scaled_e(int l,double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_bessel_kl_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for double gsl_sf_bessel_kl_scaled(int l,double x);  ohttp://www.google.com/search?q=gsl_sf_bessel_kl_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Wwrapper for int gsl_sf_bessel_kl_scaled_array(int lmax,double x,double* result_array);  uhttp://www.google.com/search?q=gsl_sf_bessel_kl_scaled_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Owrapper for int gsl_sf_bessel_Jnu_e(double nu,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_bessel_Jnu_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky :wrapper for double gsl_sf_bessel_Jnu(double nu,double x);  ihttp://www.google.com/search?q=gsl_sf_bessel_Jnu&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Owrapper for int gsl_sf_bessel_Ynu_e(double nu,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_bessel_Ynu_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky :wrapper for double gsl_sf_bessel_Ynu(double nu,double x);  ihttp://www.google.com/search?q=gsl_sf_bessel_Ynu&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky _wrapper for int gsl_sf_bessel_sequence_Jnu_e(double nu,gsl_mode_t mode,size_t size,double* v);  thttp://www.google.com/search?q=gsl_sf_bessel_sequence_Jnu_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Vwrapper for int gsl_sf_bessel_Inu_scaled_e(double nu,double x,gsl_sf_result* result);  rhttp://www.google.com/search?q=gsl_sf_bessel_Inu_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Awrapper for double gsl_sf_bessel_Inu_scaled(double nu,double x);  phttp://www.google.com/search?q=gsl_sf_bessel_Inu_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Owrapper for int gsl_sf_bessel_Inu_e(double nu,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_bessel_Inu_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky :wrapper for double gsl_sf_bessel_Inu(double nu,double x);  ihttp://www.google.com/search?q=gsl_sf_bessel_Inu&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Vwrapper for int gsl_sf_bessel_Knu_scaled_e(double nu,double x,gsl_sf_result* result);  rhttp://www.google.com/search?q=gsl_sf_bessel_Knu_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Awrapper for double gsl_sf_bessel_Knu_scaled(double nu,double x);  phttp://www.google.com/search?q=gsl_sf_bessel_Knu_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Owrapper for int gsl_sf_bessel_Knu_e(double nu,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_bessel_Knu_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky :wrapper for double gsl_sf_bessel_Knu(double nu,double x);  ihttp://www.google.com/search?q=gsl_sf_bessel_Knu&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Qwrapper for int gsl_sf_bessel_lnKnu_e(double nu,double x,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_bessel_lnKnu_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for double gsl_sf_bessel_lnKnu(double nu,double x);  khttp://www.google.com/search?q=gsl_sf_bessel_lnKnu&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_bessel_zero_J0_e(int s,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_bessel_zero_J0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_bessel_zero_J0(int s);  mhttp://www.google.com/search?q=gsl_sf_bessel_zero_J0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_bessel_zero_J1_e(int s,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_bessel_zero_J1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_bessel_zero_J1(int s);  mhttp://www.google.com/search?q=gsl_sf_bessel_zero_J1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Qwrapper for int gsl_sf_bessel_zero_Jnu_e(double nu,int s,gsl_sf_result* result);  phttp://www.google.com/search?q=gsl_sf_bessel_zero_Jnu_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for double gsl_sf_bessel_zero_Jnu(double nu,int s);  nhttp://www.google.com/search?q=gsl_sf_bessel_zero_Jnu&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky XXX uses ffi provisional!Alberto Ruiz (aruiz at um dot es)Bwrapper for int gsl_sf_clausen_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_clausen_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky -wrapper for double gsl_sf_clausen(double x);  fhttp://www.google.com/search?q=gsl_sf_clausen&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  uses ffi provisional!Alberto Ruiz (aruiz at um dot es)Qwrapper for int gsl_sf_hydrogenicR_1_e(double Z,double r,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_hydrogenicR_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for double gsl_sf_hydrogenicR_1(double Z,double r);  lhttp://www.google.com/search?q=gsl_sf_hydrogenicR_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky [wrapper for int gsl_sf_hydrogenicR_e(int n,int l,double Z,double r,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_hydrogenicR_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for double gsl_sf_hydrogenicR(int n,int l,double Z,double r);  jhttp://www.google.com/search?q=gsl_sf_hydrogenicR&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for int gsl_sf_coulomb_wave_FG_e(double eta,double x,double lam_F,int k_lam_G,gsl_sf_result* F,gsl_sf_result* Fp,gsl_sf_result* G,gsl_sf_result* Gp,double* exp_F,double* exp_G);  phttp://www.google.com/search?q=gsl_sf_coulomb_wave_FG_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ~wrapper for int gsl_sf_coulomb_wave_F_array(double lam_min,int kmax,double eta,double x,double* fc_array,double* F_exponent);  shttp://www.google.com/search?q=gsl_sf_coulomb_wave_F_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for int gsl_sf_coulomb_wave_FG_array(double lam_min,int kmax,double eta,double x,double* fc_array,double* gc_array,double* F_exponent,double* G_exponent);  thttp://www.google.com/search?q=gsl_sf_coulomb_wave_FG_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for int gsl_sf_coulomb_wave_FGp_array(double lam_min,int kmax,double eta,double x,double* fc_array,double* fcp_array,double* gc_array,double* gcp_array,double* F_exponent,double* G_exponent);  uhttp://www.google.com/search?q=gsl_sf_coulomb_wave_FGp_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for int gsl_sf_coulomb_wave_sphF_array(double lam_min,int kmax,double eta,double x,double* fc_array,double* F_exponent);  vhttp://www.google.com/search?q=gsl_sf_coulomb_wave_sphF_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Pwrapper for int gsl_sf_coulomb_CL_e(double L,double eta,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_coulomb_CL_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Uwrapper for int gsl_sf_coulomb_CL_array(double Lmin,int kmax,double eta,double* cl);  ohttp://www.google.com/search?q=gsl_sf_coulomb_CL_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)wrapper for int gsl_sf_coupling_3j_e(int two_ja,int two_jb,int two_jc,int two_ma,int two_mb,int two_mc,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_coupling_3j_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky jwrapper for double gsl_sf_coupling_3j(int two_ja,int two_jb,int two_jc,int two_ma,int two_mb,int two_mc);  jhttp://www.google.com/search?q=gsl_sf_coupling_3j&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for int gsl_sf_coupling_6j_e(int two_ja,int two_jb,int two_jc,int two_jd,int two_je,int two_jf,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_coupling_6j_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky jwrapper for double gsl_sf_coupling_6j(int two_ja,int two_jb,int two_jc,int two_jd,int two_je,int two_jf);  jhttp://www.google.com/search?q=gsl_sf_coupling_6j&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for int gsl_sf_coupling_RacahW_e(int two_ja,int two_jb,int two_jc,int two_jd,int two_je,int two_jf,gsl_sf_result* result);  phttp://www.google.com/search?q=gsl_sf_coupling_RacahW_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky nwrapper for double gsl_sf_coupling_RacahW(int two_ja,int two_jb,int two_jc,int two_jd,int two_je,int two_jf);  nhttp://www.google.com/search?q=gsl_sf_coupling_RacahW&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for int gsl_sf_coupling_9j_e(int two_ja,int two_jb,int two_jc,int two_jd,int two_je,int two_jf,int two_jg,int two_jh,int two_ji,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_coupling_9j_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for double gsl_sf_coupling_9j(int two_ja,int two_jb,int two_jc,int two_jd,int two_je,int two_jf,int two_jg,int two_jh,int two_ji);  jhttp://www.google.com/search?q=gsl_sf_coupling_9j&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky wrapper for int gsl_sf_coupling_6j_INCORRECT_e(int two_ja,int two_jb,int two_jc,int two_jd,int two_je,int two_jf,gsl_sf_result* result);  vhttp://www.google.com/search?q=gsl_sf_coupling_6j_INCORRECT_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky twrapper for double gsl_sf_coupling_6j_INCORRECT(int two_ja,int two_jb,int two_jc,int two_jd,int two_je,int two_jf);  thttp://www.google.com/search?q=gsl_sf_coupling_6j_INCORRECT&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)Awrapper for int gsl_sf_dawson_e(double x,gsl_sf_result* result);  ghttp://www.google.com/search?q=gsl_sf_dawson_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ,wrapper for double gsl_sf_dawson(double x);  ehttp://www.google.com/search?q=gsl_sf_dawson&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)     Bwrapper for int gsl_sf_debye_1_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_debye_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky -wrapper for double gsl_sf_debye_1(double x);  fhttp://www.google.com/search?q=gsl_sf_debye_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for int gsl_sf_debye_2_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_debye_2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  -wrapper for double gsl_sf_debye_2(double x);  fhttp://www.google.com/search?q=gsl_sf_debye_2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  Bwrapper for int gsl_sf_debye_3_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_debye_3_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  -wrapper for double gsl_sf_debye_3(double x);  fhttp://www.google.com/search?q=gsl_sf_debye_3&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  Bwrapper for int gsl_sf_debye_4_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_debye_4_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  -wrapper for double gsl_sf_debye_4(double x);  fhttp://www.google.com/search?q=gsl_sf_debye_4&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for int gsl_sf_debye_5_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_debye_5_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky -wrapper for double gsl_sf_debye_5(double x);  fhttp://www.google.com/search?q=gsl_sf_debye_5&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for int gsl_sf_debye_6_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_debye_6_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky -wrapper for double gsl_sf_debye_6(double x);  fhttp://www.google.com/search?q=gsl_sf_debye_6&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky                  uses ffi provisional!Alberto Ruiz (aruiz at um dot es) @wrapper for int gsl_sf_dilog_e(double x,gsl_sf_result* result);  fhttp://www.google.com/search?q=gsl_sf_dilog_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky +wrapper for double gsl_sf_dilog(double x);  dhttp://www.google.com/search?q=gsl_sf_dilog&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky pwrapper for int gsl_sf_complex_dilog_xy_e(double x,double y,gsl_sf_result* result_re,gsl_sf_result* result_im);  qhttp://www.google.com/search?q=gsl_sf_complex_dilog_xy_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky qwrapper for int gsl_sf_complex_dilog_e(double r,double theta,gsl_sf_result* result_re,gsl_sf_result* result_im);  nhttp://www.google.com/search?q=gsl_sf_complex_dilog_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky mwrapper for int gsl_sf_complex_spence_xy_e(double x,double y,gsl_sf_result* real_sp,gsl_sf_result* imag_sp);  rhttp://www.google.com/search?q=gsl_sf_complex_spence_xy_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)Lwrapper for int gsl_sf_multiply_e(double x,double y,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_multiply_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 7wrapper for double gsl_sf_multiply(double x,double y);  ghttp://www.google.com/search?q=gsl_sf_multiply&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky dwrapper for int gsl_sf_multiply_err_e(double x,double dx,double y,double dy,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_multiply_err_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)0 !"#$%&'()*+,-./012Wwrapper for int gsl_sf_ellint_Kcomp_e(double k,gsl_mode_t mode,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_ellint_Kcomp_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for double gsl_sf_ellint_Kcomp(double k,gsl_mode_t mode);  khttp://www.google.com/search?q=gsl_sf_ellint_Kcomp&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Wwrapper for int gsl_sf_ellint_Ecomp_e(double k,gsl_mode_t mode,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_ellint_Ecomp_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for double gsl_sf_ellint_Ecomp(double k,gsl_mode_t mode);  khttp://www.google.com/search?q=gsl_sf_ellint_Ecomp&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky `wrapper for int gsl_sf_ellint_Pcomp_e(double k,double n,gsl_mode_t mode,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_ellint_Pcomp_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for double gsl_sf_ellint_Pcomp(double k,double n,gsl_mode_t mode);  khttp://www.google.com/search?q=gsl_sf_ellint_Pcomp&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Wwrapper for int gsl_sf_ellint_Dcomp_e(double k,gsl_mode_t mode,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_ellint_Dcomp_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for double gsl_sf_ellint_Dcomp(double k,gsl_mode_t mode);  khttp://www.google.com/search?q=gsl_sf_ellint_Dcomp&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ^wrapper for int gsl_sf_ellint_F_e(double phi,double k,gsl_mode_t mode,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_ellint_F_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  Iwrapper for double gsl_sf_ellint_F(double phi,double k,gsl_mode_t mode);  ghttp://www.google.com/search?q=gsl_sf_ellint_F&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky !^wrapper for int gsl_sf_ellint_E_e(double phi,double k,gsl_mode_t mode,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_ellint_E_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky "Iwrapper for double gsl_sf_ellint_E(double phi,double k,gsl_mode_t mode);  ghttp://www.google.com/search?q=gsl_sf_ellint_E&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky #gwrapper for int gsl_sf_ellint_P_e(double phi,double k,double n,gsl_mode_t mode,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_ellint_P_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky $Rwrapper for double gsl_sf_ellint_P(double phi,double k,double n,gsl_mode_t mode);  ghttp://www.google.com/search?q=gsl_sf_ellint_P&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky %gwrapper for int gsl_sf_ellint_D_e(double phi,double k,double n,gsl_mode_t mode,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_ellint_D_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky &Rwrapper for double gsl_sf_ellint_D(double phi,double k,double n,gsl_mode_t mode);  ghttp://www.google.com/search?q=gsl_sf_ellint_D&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ']wrapper for int gsl_sf_ellint_RC_e(double x,double y,gsl_mode_t mode,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_ellint_RC_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky (Hwrapper for double gsl_sf_ellint_RC(double x,double y,gsl_mode_t mode);  hhttp://www.google.com/search?q=gsl_sf_ellint_RC&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky )fwrapper for int gsl_sf_ellint_RD_e(double x,double y,double z,gsl_mode_t mode,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_ellint_RD_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky *Qwrapper for double gsl_sf_ellint_RD(double x,double y,double z,gsl_mode_t mode);  hhttp://www.google.com/search?q=gsl_sf_ellint_RD&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky +fwrapper for int gsl_sf_ellint_RF_e(double x,double y,double z,gsl_mode_t mode,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_ellint_RF_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ,Qwrapper for double gsl_sf_ellint_RF(double x,double y,double z,gsl_mode_t mode);  hhttp://www.google.com/search?q=gsl_sf_ellint_RF&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky -owrapper for int gsl_sf_ellint_RJ_e(double x,double y,double z,double p,gsl_mode_t mode,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_ellint_RJ_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky .Zwrapper for double gsl_sf_ellint_RJ(double x,double y,double z,double p,gsl_mode_t mode);  hhttp://www.google.com/search?q=gsl_sf_ellint_RJ&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  !"#$%&'()*+,-. !"#$%&'()*+,-. !"#$%&'()*+,-.uses ffi provisional!Alberto Ruiz (aruiz at um dot es)3456789:;<=>/?wrapper for int gsl_sf_erfc_e(double x,gsl_sf_result* result);  ehttp://www.google.com/search?q=gsl_sf_erfc_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 0*wrapper for double gsl_sf_erfc(double x);  chttp://www.google.com/search?q=gsl_sf_erfc&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1Cwrapper for int gsl_sf_log_erfc_e(double x,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_log_erfc_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 2.wrapper for double gsl_sf_log_erfc(double x);  ghttp://www.google.com/search?q=gsl_sf_log_erfc&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 3>wrapper for int gsl_sf_erf_e(double x,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_erf_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 4)wrapper for double gsl_sf_erf(double x);  bhttp://www.google.com/search?q=gsl_sf_erf&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5@wrapper for int gsl_sf_erf_Z_e(double x,gsl_sf_result* result);  fhttp://www.google.com/search?q=gsl_sf_erf_Z_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 6@wrapper for int gsl_sf_erf_Q_e(double x,gsl_sf_result* result);  fhttp://www.google.com/search?q=gsl_sf_erf_Q_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 7+wrapper for double gsl_sf_erf_Z(double x);  dhttp://www.google.com/search?q=gsl_sf_erf_Z&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 8+wrapper for double gsl_sf_erf_Q(double x);  dhttp://www.google.com/search?q=gsl_sf_erf_Q&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 9Awrapper for int gsl_sf_hazard_e(double x,gsl_sf_result* result);  ghttp://www.google.com/search?q=gsl_sf_hazard_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky :,wrapper for double gsl_sf_hazard(double x);  ehttp://www.google.com/search?q=gsl_sf_hazard&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /0123456789: /0123456789: /0123456789:uses ffi provisional!Alberto Ruiz (aruiz at um dot es)&?@ABCDEFGHIJKLMNOPQ;>wrapper for int gsl_sf_exp_e(double x,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_exp_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <)wrapper for double gsl_sf_exp(double x);  bhttp://www.google.com/search?q=gsl_sf_exp&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky =Fwrapper for int gsl_sf_exp_e10_e(double x,gsl_sf_result_e10* result);  hhttp://www.google.com/search?q=gsl_sf_exp_e10_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky >Lwrapper for int gsl_sf_exp_mult_e(double x,double y,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_exp_mult_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ?7wrapper for double gsl_sf_exp_mult(double x,double y);  ghttp://www.google.com/search?q=gsl_sf_exp_mult&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky @Twrapper for int gsl_sf_exp_mult_e10_e(double x,double y,gsl_sf_result_e10* result);  mhttp://www.google.com/search?q=gsl_sf_exp_mult_e10_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky A@wrapper for int gsl_sf_expm1_e(double x,gsl_sf_result* result);  fhttp://www.google.com/search?q=gsl_sf_expm1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky B+wrapper for double gsl_sf_expm1(double x);  dhttp://www.google.com/search?q=gsl_sf_expm1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky CAwrapper for int gsl_sf_exprel_e(double x,gsl_sf_result* result);  ghttp://www.google.com/search?q=gsl_sf_exprel_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky D,wrapper for double gsl_sf_exprel(double x);  ehttp://www.google.com/search?q=gsl_sf_exprel&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ECwrapper for int gsl_sf_exprel_2_e(double x,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_exprel_2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky F.wrapper for double gsl_sf_exprel_2(double x);  ghttp://www.google.com/search?q=gsl_sf_exprel_2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky GIwrapper for int gsl_sf_exprel_n_e(int n,double x,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_exprel_n_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky H4wrapper for double gsl_sf_exprel_n(int n,double x);  ghttp://www.google.com/search?q=gsl_sf_exprel_n&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky IOwrapper for int gsl_sf_exprel_n_CF_e(double n,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_exprel_n_CF_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky JLwrapper for int gsl_sf_exp_err_e(double x,double dx,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_exp_err_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky KTwrapper for int gsl_sf_exp_err_e10_e(double x,double dx,gsl_sf_result_e10* result);  lhttp://www.google.com/search?q=gsl_sf_exp_err_e10_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ldwrapper for int gsl_sf_exp_mult_err_e(double x,double dx,double y,double dy,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_exp_mult_err_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Mlwrapper for int gsl_sf_exp_mult_err_e10_e(double x,double dx,double y,double dy,gsl_sf_result_e10* result);  qhttp://www.google.com/search?q=gsl_sf_exp_mult_err_e10_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ;<=>?@ABCDEFGHIJKLM;<=>?@ABCDEFGHIJKLM;<=>?@ABCDEFGHIJKLMuses ffi provisional!Alberto Ruiz (aruiz at um dot es)8RSTUVWXYZ[\]^_`abcdefghijklmNDwrapper for int gsl_sf_expint_E1_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_expint_E1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky O/wrapper for double gsl_sf_expint_E1(double x);  hhttp://www.google.com/search?q=gsl_sf_expint_E1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky PDwrapper for int gsl_sf_expint_E2_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_expint_E2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Q/wrapper for double gsl_sf_expint_E2(double x);  hhttp://www.google.com/search?q=gsl_sf_expint_E2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky RJwrapper for int gsl_sf_expint_En_e(int n,double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_expint_En_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky S5wrapper for double gsl_sf_expint_En(int n,double x);  hhttp://www.google.com/search?q=gsl_sf_expint_En&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky TKwrapper for int gsl_sf_expint_E1_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_expint_E1_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky U6wrapper for double gsl_sf_expint_E1_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_expint_E1_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky VKwrapper for int gsl_sf_expint_E2_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_expint_E2_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky W6wrapper for double gsl_sf_expint_E2_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_expint_E2_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky XQwrapper for int gsl_sf_expint_En_scaled_e(int n,double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_expint_En_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Y<wrapper for double gsl_sf_expint_En_scaled(int n,double x);  ohttp://www.google.com/search?q=gsl_sf_expint_En_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ZDwrapper for int gsl_sf_expint_Ei_e(double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_expint_Ei_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky [/wrapper for double gsl_sf_expint_Ei(double x);  hhttp://www.google.com/search?q=gsl_sf_expint_Ei&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky \Kwrapper for int gsl_sf_expint_Ei_scaled_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_expint_Ei_scaled_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ]6wrapper for double gsl_sf_expint_Ei_scaled(double x);  ohttp://www.google.com/search?q=gsl_sf_expint_Ei_scaled&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ^>wrapper for int gsl_sf_Shi_e(double x,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_Shi_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky _)wrapper for double gsl_sf_Shi(double x);  bhttp://www.google.com/search?q=gsl_sf_Shi&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky `>wrapper for int gsl_sf_Chi_e(double x,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_Chi_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky a)wrapper for double gsl_sf_Chi(double x);  bhttp://www.google.com/search?q=gsl_sf_Chi&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky bCwrapper for int gsl_sf_expint_3_e(double x,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_expint_3_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky c.wrapper for double gsl_sf_expint_3(double x);  ghttp://www.google.com/search?q=gsl_sf_expint_3&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky d=wrapper for int gsl_sf_Si_e(double x,gsl_sf_result* result);  chttp://www.google.com/search?q=gsl_sf_Si_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky e(wrapper for double gsl_sf_Si(double x);  ahttp://www.google.com/search?q=gsl_sf_Si&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky f=wrapper for int gsl_sf_Ci_e(double x,gsl_sf_result* result);  chttp://www.google.com/search?q=gsl_sf_Ci_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky g(wrapper for double gsl_sf_Ci(double x);  ahttp://www.google.com/search?q=gsl_sf_Ci&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky hBwrapper for int gsl_sf_atanint_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_atanint_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky i-wrapper for double gsl_sf_atanint(double x);  fhttp://www.google.com/search?q=gsl_sf_atanint&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky NOPQRSTUVWXYZ[\]^_`abcdefghiNOPQRSTUVWXYZ[\]^_`abcdefghiNOPQRSTUVWXYZ[\]^_`abcdefghiuses ffi provisional!Alberto Ruiz (aruiz at um dot es)$nopqrstuvwxyz{|}~jIwrapper for int gsl_sf_fermi_dirac_m1_e(double x,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_fermi_dirac_m1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky k4wrapper for double gsl_sf_fermi_dirac_m1(double x);  mhttp://www.google.com/search?q=gsl_sf_fermi_dirac_m1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky lHwrapper for int gsl_sf_fermi_dirac_0_e(double x,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_fermi_dirac_0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky m3wrapper for double gsl_sf_fermi_dirac_0(double x);  lhttp://www.google.com/search?q=gsl_sf_fermi_dirac_0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky nHwrapper for int gsl_sf_fermi_dirac_1_e(double x,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_fermi_dirac_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky o3wrapper for double gsl_sf_fermi_dirac_1(double x);  lhttp://www.google.com/search?q=gsl_sf_fermi_dirac_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky pHwrapper for int gsl_sf_fermi_dirac_2_e(double x,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_fermi_dirac_2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky q3wrapper for double gsl_sf_fermi_dirac_2(double x);  lhttp://www.google.com/search?q=gsl_sf_fermi_dirac_2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky rPwrapper for int gsl_sf_fermi_dirac_int_e(int j,double x,gsl_sf_result* result);  phttp://www.google.com/search?q=gsl_sf_fermi_dirac_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky s;wrapper for double gsl_sf_fermi_dirac_int(int j,double x);  nhttp://www.google.com/search?q=gsl_sf_fermi_dirac_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky tLwrapper for int gsl_sf_fermi_dirac_mhalf_e(double x,gsl_sf_result* result);  rhttp://www.google.com/search?q=gsl_sf_fermi_dirac_mhalf_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky u7wrapper for double gsl_sf_fermi_dirac_mhalf(double x);  phttp://www.google.com/search?q=gsl_sf_fermi_dirac_mhalf&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky vKwrapper for int gsl_sf_fermi_dirac_half_e(double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_fermi_dirac_half_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky w6wrapper for double gsl_sf_fermi_dirac_half(double x);  ohttp://www.google.com/search?q=gsl_sf_fermi_dirac_half&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky xLwrapper for int gsl_sf_fermi_dirac_3half_e(double x,gsl_sf_result* result);  rhttp://www.google.com/search?q=gsl_sf_fermi_dirac_3half_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky y7wrapper for double gsl_sf_fermi_dirac_3half(double x);  phttp://www.google.com/search?q=gsl_sf_fermi_dirac_3half&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky zUwrapper for int gsl_sf_fermi_dirac_inc_0_e(double x,double b,gsl_sf_result* result);  rhttp://www.google.com/search?q=gsl_sf_fermi_dirac_inc_0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky {@wrapper for double gsl_sf_fermi_dirac_inc_0(double x,double b);  phttp://www.google.com/search?q=gsl_sf_fermi_dirac_inc_0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky jklmnopqrstuvwxyz{jklmnopqrstuvwxyz{jklmnopqrstuvwxyz{uses ffi provisional!Alberto Ruiz (aruiz at um dot es)X|Bwrapper for int gsl_sf_lngamma_e(double x,gsl_sf_result* result); 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 hhttp://www.google.com/search?q=gsl_sf_gammastar&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Cwrapper for int gsl_sf_gammainv_e(double x,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_gammainv_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky .wrapper for double gsl_sf_gammainv(double x);  ghttp://www.google.com/search?q=gsl_sf_gammainv&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ewrapper for int gsl_sf_lngamma_complex_e(double zr,double zi,gsl_sf_result* lnr,gsl_sf_result* arg);  phttp://www.google.com/search?q=gsl_sf_lngamma_complex_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Lwrapper for int gsl_sf_taylorcoeff_e(int n,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_taylorcoeff_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 7wrapper for double gsl_sf_taylorcoeff(int n,double x);  jhttp://www.google.com/search?q=gsl_sf_taylorcoeff&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for int gsl_sf_fact_e(int n,gsl_sf_result* result);  ehttp://www.google.com/search?q=gsl_sf_fact_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 'wrapper for double gsl_sf_fact(int n);  chttp://www.google.com/search?q=gsl_sf_fact&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for int gsl_sf_doublefact_e(int n,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_doublefact_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky -wrapper for double gsl_sf_doublefact(int n);  ihttp://www.google.com/search?q=gsl_sf_doublefact&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky >wrapper for int gsl_sf_lnfact_e(int n,gsl_sf_result* result);  ghttp://www.google.com/search?q=gsl_sf_lnfact_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky )wrapper for double gsl_sf_lnfact(int n);  ehttp://www.google.com/search?q=gsl_sf_lnfact&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for int gsl_sf_lndoublefact_e(int n,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_lndoublefact_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky /wrapper for double gsl_sf_lndoublefact(int n); 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 lhttp://www.google.com/search?q=gsl_sf_gamma_inc_Q_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky :wrapper for double gsl_sf_gamma_inc_Q(double a,double x);  jhttp://www.google.com/search?q=gsl_sf_gamma_inc_Q&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Owrapper for int gsl_sf_gamma_inc_P_e(double a,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_gamma_inc_P_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky :wrapper for double gsl_sf_gamma_inc_P(double a,double x);  jhttp://www.google.com/search?q=gsl_sf_gamma_inc_P&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Mwrapper for int gsl_sf_gamma_inc_e(double a,double x,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_gamma_inc_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 8wrapper for double gsl_sf_gamma_inc(double a,double x);  hhttp://www.google.com/search?q=gsl_sf_gamma_inc&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for int gsl_sf_lnbeta_e(double a,double b,gsl_sf_result* result);  ghttp://www.google.com/search?q=gsl_sf_lnbeta_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 5wrapper for double gsl_sf_lnbeta(double a,double b);  ehttp://www.google.com/search?q=gsl_sf_lnbeta&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Zwrapper for int gsl_sf_lnbeta_sgn_e(double x,double y,gsl_sf_result* result,double* sgn);  khttp://www.google.com/search?q=gsl_sf_lnbeta_sgn_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Hwrapper for int gsl_sf_beta_e(double a,double b,gsl_sf_result* result);  ehttp://www.google.com/search?q=gsl_sf_beta_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 3wrapper for double gsl_sf_beta(double a,double b);  chttp://www.google.com/search?q=gsl_sf_beta&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Uwrapper for int gsl_sf_beta_inc_e(double a,double b,double x,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_beta_inc_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky @wrapper for double gsl_sf_beta_inc(double a,double b,double x);  ghttp://www.google.com/search?q=gsl_sf_beta_inc&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky (|}~(|}~(|}~uses ffi provisional!Alberto Ruiz (aruiz at um dot es)Twrapper for int gsl_sf_gegenpoly_1_e(double lambda,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_gegenpoly_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Twrapper for int gsl_sf_gegenpoly_2_e(double lambda,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_gegenpoly_2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Twrapper for int gsl_sf_gegenpoly_3_e(double lambda,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_gegenpoly_3_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ?wrapper for double gsl_sf_gegenpoly_1(double lambda,double x);  jhttp://www.google.com/search?q=gsl_sf_gegenpoly_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ?wrapper for double gsl_sf_gegenpoly_2(double lambda,double x);  jhttp://www.google.com/search?q=gsl_sf_gegenpoly_2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ?wrapper for double gsl_sf_gegenpoly_3(double lambda,double x);  jhttp://www.google.com/search?q=gsl_sf_gegenpoly_3&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Zwrapper for int gsl_sf_gegenpoly_n_e(int n,double lambda,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_gegenpoly_n_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ewrapper for double gsl_sf_gegenpoly_n(int n,double lambda,double x);  jhttp://www.google.com/search?q=gsl_sf_gegenpoly_n&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ^wrapper for int gsl_sf_gegenpoly_array(int nmax,double lambda,double x,double* result_array);  nhttp://www.google.com/search?q=gsl_sf_gegenpoly_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es),Nwrapper for int gsl_sf_hyperg_0F1_e(double c,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_hyperg_0F1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 9wrapper for double gsl_sf_hyperg_0F1(double c,double x);  ihttp://www.google.com/search?q=gsl_sf_hyperg_0F1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Uwrapper for int gsl_sf_hyperg_1F1_int_e(int m,int n,double x,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_hyperg_1F1_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky @wrapper for double gsl_sf_hyperg_1F1_int(int m,int n,double x);  mhttp://www.google.com/search?q=gsl_sf_hyperg_1F1_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Wwrapper for int gsl_sf_hyperg_1F1_e(double a,double b,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_hyperg_1F1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for double gsl_sf_hyperg_1F1(double a,double b,double x);  ihttp://www.google.com/search?q=gsl_sf_hyperg_1F1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Swrapper for int gsl_sf_hyperg_U_int_e(int m,int n,double x,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_hyperg_U_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky >wrapper for double gsl_sf_hyperg_U_int(int m,int n,double x);  khttp://www.google.com/search?q=gsl_sf_hyperg_U_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky [wrapper for int gsl_sf_hyperg_U_int_e10_e(int m,int n,double x,gsl_sf_result_e10* result);  qhttp://www.google.com/search?q=gsl_sf_hyperg_U_int_e10_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Uwrapper for int gsl_sf_hyperg_U_e(double a,double b,double x,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_hyperg_U_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky @wrapper for double gsl_sf_hyperg_U(double a,double b,double x);  ghttp://www.google.com/search?q=gsl_sf_hyperg_U&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ]wrapper for int gsl_sf_hyperg_U_e10_e(double a,double b,double x,gsl_sf_result_e10* result);  mhttp://www.google.com/search?q=gsl_sf_hyperg_U_e10_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky `wrapper for int gsl_sf_hyperg_2F1_e(double a,double b,double c,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_hyperg_2F1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Kwrapper for double gsl_sf_hyperg_2F1(double a,double b,double c,double x);  ihttp://www.google.com/search?q=gsl_sf_hyperg_2F1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky gwrapper for int gsl_sf_hyperg_2F1_conj_e(double aR,double aI,double c,double x,gsl_sf_result* result);  phttp://www.google.com/search?q=gsl_sf_hyperg_2F1_conj_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Rwrapper for double gsl_sf_hyperg_2F1_conj(double aR,double aI,double c,double x);  nhttp://www.google.com/search?q=gsl_sf_hyperg_2F1_conj&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky gwrapper for int gsl_sf_hyperg_2F1_renorm_e(double a,double b,double c,double x,gsl_sf_result* result);  rhttp://www.google.com/search?q=gsl_sf_hyperg_2F1_renorm_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Rwrapper for double gsl_sf_hyperg_2F1_renorm(double a,double b,double c,double x);  phttp://www.google.com/search?q=gsl_sf_hyperg_2F1_renorm&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky nwrapper for int gsl_sf_hyperg_2F1_conj_renorm_e(double aR,double aI,double c,double x,gsl_sf_result* result);  whttp://www.google.com/search?q=gsl_sf_hyperg_2F1_conj_renorm_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for double gsl_sf_hyperg_2F1_conj_renorm(double aR,double aI,double c,double x);  uhttp://www.google.com/search?q=gsl_sf_hyperg_2F1_conj_renorm&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Wwrapper for int gsl_sf_hyperg_2F0_e(double a,double b,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_hyperg_2F0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for double gsl_sf_hyperg_2F0(double a,double b,double x);  ihttp://www.google.com/search?q=gsl_sf_hyperg_2F0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)Nwrapper for int gsl_sf_laguerre_1_e(double a,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_laguerre_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Nwrapper for int gsl_sf_laguerre_2_e(double a,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_laguerre_2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Nwrapper for int gsl_sf_laguerre_3_e(double a,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_laguerre_3_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 9wrapper for double gsl_sf_laguerre_1(double a,double x);  ihttp://www.google.com/search?q=gsl_sf_laguerre_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 9wrapper for double gsl_sf_laguerre_2(double a,double x);  ihttp://www.google.com/search?q=gsl_sf_laguerre_2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 9wrapper for double gsl_sf_laguerre_3(double a,double x);  ihttp://www.google.com/search?q=gsl_sf_laguerre_3&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Twrapper for int gsl_sf_laguerre_n_e(int n,double a,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_laguerre_n_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ?wrapper for double gsl_sf_laguerre_n(int n,double a,double x);  ihttp://www.google.com/search?q=gsl_sf_laguerre_n&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)Ewrapper for int gsl_sf_lambert_W0_e(double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_lambert_W0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 0wrapper for double gsl_sf_lambert_W0(double x);  ihttp://www.google.com/search?q=gsl_sf_lambert_W0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_lambert_Wm1_e(double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_lambert_Wm1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_lambert_Wm1(double x);  jhttp://www.google.com/search?q=gsl_sf_lambert_Wm1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)XLwrapper for int gsl_sf_legendre_Pl_e(int l,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_legendre_Pl_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 7wrapper for double gsl_sf_legendre_Pl(int l,double x);  jhttp://www.google.com/search?q=gsl_sf_legendre_Pl&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Rwrapper for int gsl_sf_legendre_Pl_array(int lmax,double x,double* result_array);  phttp://www.google.com/search?q=gsl_sf_legendre_Pl_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  swrapper for int gsl_sf_legendre_Pl_deriv_array(int lmax,double x,double* result_array,double* result_deriv_array);  vhttp://www.google.com/search?q=gsl_sf_legendre_Pl_deriv_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_legendre_P1_e(double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_legendre_P1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_legendre_P2_e(double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_legendre_P2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_legendre_P3_e(double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_legendre_P3_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_legendre_P1(double x);  jhttp://www.google.com/search?q=gsl_sf_legendre_P1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_legendre_P2(double x);  jhttp://www.google.com/search?q=gsl_sf_legendre_P2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_legendre_P3(double x);  jhttp://www.google.com/search?q=gsl_sf_legendre_P3&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_legendre_Q0_e(double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_legendre_Q0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_legendre_Q0(double x);  jhttp://www.google.com/search?q=gsl_sf_legendre_Q0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_legendre_Q1_e(double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_legendre_Q1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_legendre_Q1(double x);  jhttp://www.google.com/search?q=gsl_sf_legendre_Q1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Lwrapper for int gsl_sf_legendre_Ql_e(int l,double x,gsl_sf_result* result);  lhttp://www.google.com/search?q=gsl_sf_legendre_Ql_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 7wrapper for double gsl_sf_legendre_Ql(int l,double x);  jhttp://www.google.com/search?q=gsl_sf_legendre_Ql&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Swrapper for int gsl_sf_legendre_Plm_e(int l,int m,double x,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_legendre_Plm_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky >wrapper for double gsl_sf_legendre_Plm(int l,int m,double x);  khttp://www.google.com/search?q=gsl_sf_legendre_Plm&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  Ywrapper for int gsl_sf_legendre_Plm_array(int lmax,int m,double x,double* result_array);  qhttp://www.google.com/search?q=gsl_sf_legendre_Plm_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  zwrapper for int gsl_sf_legendre_Plm_deriv_array(int lmax,int m,double x,double* result_array,double* result_deriv_array);  whttp://www.google.com/search?q=gsl_sf_legendre_Plm_deriv_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Vwrapper for int gsl_sf_legendre_sphPlm_e(int l,int m,double x,gsl_sf_result* result);  phttp://www.google.com/search?q=gsl_sf_legendre_sphPlm_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Awrapper for double gsl_sf_legendre_sphPlm(int l,int m,double x);  nhttp://www.google.com/search?q=gsl_sf_legendre_sphPlm&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  \wrapper for int gsl_sf_legendre_sphPlm_array(int lmax,int m,double x,double* result_array);  thttp://www.google.com/search?q=gsl_sf_legendre_sphPlm_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  }wrapper for int gsl_sf_legendre_sphPlm_deriv_array(int lmax,int m,double x,double* result_array,double* result_deriv_array);  zhttp://www.google.com/search?q=gsl_sf_legendre_sphPlm_deriv_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for int gsl_sf_legendre_array_size(int lmax,int m);  rhttp://www.google.com/search?q=gsl_sf_legendre_array_size&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Vwrapper for int gsl_sf_conicalP_half_e(double lambda,double x,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_conicalP_half_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Awrapper for double gsl_sf_conicalP_half(double lambda,double x);  lhttp://www.google.com/search?q=gsl_sf_conicalP_half&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Wwrapper for int gsl_sf_conicalP_mhalf_e(double lambda,double x,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_conicalP_mhalf_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for double gsl_sf_conicalP_mhalf(double lambda,double x);  mhttp://www.google.com/search?q=gsl_sf_conicalP_mhalf&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Swrapper for int gsl_sf_conicalP_0_e(double lambda,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_conicalP_0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky >wrapper for double gsl_sf_conicalP_0(double lambda,double x);  ihttp://www.google.com/search?q=gsl_sf_conicalP_0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Swrapper for int gsl_sf_conicalP_1_e(double lambda,double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_conicalP_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky >wrapper for double gsl_sf_conicalP_1(double lambda,double x);  ihttp://www.google.com/search?q=gsl_sf_conicalP_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky _wrapper for int gsl_sf_conicalP_sph_reg_e(int l,double lambda,double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_conicalP_sph_reg_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for double gsl_sf_conicalP_sph_reg(int l,double lambda,double x);  ohttp://www.google.com/search?q=gsl_sf_conicalP_sph_reg&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky _wrapper for int gsl_sf_conicalP_cyl_reg_e(int m,double lambda,double x,gsl_sf_result* result);  qhttp://www.google.com/search?q=gsl_sf_conicalP_cyl_reg_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Jwrapper for double gsl_sf_conicalP_cyl_reg(int m,double lambda,double x);  ohttp://www.google.com/search?q=gsl_sf_conicalP_cyl_reg&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for int gsl_sf_legendre_H3d_0_e(double lambda,double eta,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_legendre_H3d_0_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for double gsl_sf_legendre_H3d_0(double lambda,double eta);  mhttp://www.google.com/search?q=gsl_sf_legendre_H3d_0&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ywrapper for int gsl_sf_legendre_H3d_1_e(double lambda,double eta,gsl_sf_result* result);  ohttp://www.google.com/search?q=gsl_sf_legendre_H3d_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Dwrapper for double gsl_sf_legendre_H3d_1(double lambda,double eta);  mhttp://www.google.com/search?q=gsl_sf_legendre_H3d_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ]wrapper for int gsl_sf_legendre_H3d_e(int l,double lambda,double eta,gsl_sf_result* result);  mhttp://www.google.com/search?q=gsl_sf_legendre_H3d_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Hwrapper for double gsl_sf_legendre_H3d(int l,double lambda,double eta);  khttp://www.google.com/search?q=gsl_sf_legendre_H3d&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky cwrapper for int gsl_sf_legendre_H3d_array(int lmax,double lambda,double eta,double* result_array);  qhttp://www.google.com/search?q=gsl_sf_legendre_H3d_array&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky %%%uses ffi provisional!Alberto Ruiz (aruiz at um dot es)>wrapper for int gsl_sf_log_e(double x,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_log_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky )wrapper for double gsl_sf_log(double x);  bhttp://www.google.com/search?q=gsl_sf_log&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Bwrapper for int gsl_sf_log_abs_e(double x,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_log_abs_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky -wrapper for double gsl_sf_log_abs(double x);  fhttp://www.google.com/search?q=gsl_sf_log_abs&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky cwrapper for int gsl_sf_complex_log_e(double zr,double zi,gsl_sf_result* lnr,gsl_sf_result* theta);  lhttp://www.google.com/search?q=gsl_sf_complex_log_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Ewrapper for int gsl_sf_log_1plusx_e(double x,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_log_1plusx_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 0wrapper for double gsl_sf_log_1plusx(double x);  ihttp://www.google.com/search?q=gsl_sf_log_1plusx&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Hwrapper for int gsl_sf_log_1plusx_mx_e(double x,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_log_1plusx_mx_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 3wrapper for double gsl_sf_log_1plusx_mx(double x);  lhttp://www.google.com/search?q=gsl_sf_log_1plusx_mx&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky uses ffi provisional!Alberto Ruiz (aruiz at um dot es)Hwrapper for int gsl_sf_pow_int_e(double x,int n,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_pow_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 3wrapper for double gsl_sf_pow_int(double x,int n);  fhttp://www.google.com/search?q=gsl_sf_pow_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  uses ffi provisional!Alberto Ruiz (aruiz at um dot es) !"#$%&'?wrapper for int gsl_sf_psi_int_e(int n,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_psi_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky *wrapper for double gsl_sf_psi_int(int n);  fhttp://www.google.com/search?q=gsl_sf_psi_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky >wrapper for int gsl_sf_psi_e(double x,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_psi_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky )wrapper for double gsl_sf_psi(double x);  bhttp://www.google.com/search?q=gsl_sf_psi&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Cwrapper for int gsl_sf_psi_1piy_e(double y,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_psi_1piy_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky .wrapper for double gsl_sf_psi_1piy(double y);  ghttp://www.google.com/search?q=gsl_sf_psi_1piy&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky (kwrapper for int gsl_sf_complex_psi_e(double x,double y,gsl_sf_result* result_re,gsl_sf_result* result_im);  lhttp://www.google.com/search?q=gsl_sf_complex_psi_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Awrapper for int gsl_sf_psi_1_int_e(int n,gsl_sf_result* result);  jhttp://www.google.com/search?q=gsl_sf_psi_1_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ,wrapper for double gsl_sf_psi_1_int(int n);  hhttp://www.google.com/search?q=gsl_sf_psi_1_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky @wrapper for int gsl_sf_psi_1_e(double x,gsl_sf_result* result);  fhttp://www.google.com/search?q=gsl_sf_psi_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky +wrapper for double gsl_sf_psi_1(double x);  dhttp://www.google.com/search?q=gsl_sf_psi_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fwrapper for int gsl_sf_psi_n_e(int n,double x,gsl_sf_result* result);  fhttp://www.google.com/search?q=gsl_sf_psi_n_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 1wrapper for double gsl_sf_psi_n(int n,double x);  dhttp://www.google.com/search?q=gsl_sf_psi_n&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky   !uses ffi provisional!Alberto Ruiz (aruiz at um dot es))*+, Hwrapper for int gsl_sf_synchrotron_1_e(double x,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_synchrotron_1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  3wrapper for double gsl_sf_synchrotron_1(double x);  lhttp://www.google.com/search?q=gsl_sf_synchrotron_1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  Hwrapper for int gsl_sf_synchrotron_2_e(double x,gsl_sf_result* result);  nhttp://www.google.com/search?q=gsl_sf_synchrotron_2_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  3wrapper for double gsl_sf_synchrotron_2(double x);  lhttp://www.google.com/search?q=gsl_sf_synchrotron_2&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky             "uses ffi provisional!Alberto Ruiz (aruiz at um dot es)2-./0123456789:;<=>?@ABCDE >wrapper for int gsl_sf_sin_e(double x,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_sin_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky )wrapper for double gsl_sf_sin(double x);  bhttp://www.google.com/search?q=gsl_sf_sin&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky >wrapper for int gsl_sf_cos_e(double x,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_cos_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky )wrapper for double gsl_sf_cos(double x);  bhttp://www.google.com/search?q=gsl_sf_cos&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Iwrapper for int gsl_sf_hypot_e(double x,double y,gsl_sf_result* result);  fhttp://www.google.com/search?q=gsl_sf_hypot_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 4wrapper for double gsl_sf_hypot(double x,double y);  dhttp://www.google.com/search?q=gsl_sf_hypot&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Fawrapper for int gsl_sf_complex_sin_e(double zr,double zi,gsl_sf_result* szr,gsl_sf_result* szi);  lhttp://www.google.com/search?q=gsl_sf_complex_sin_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Gawrapper for int gsl_sf_complex_cos_e(double zr,double zi,gsl_sf_result* czr,gsl_sf_result* czi);  lhttp://www.google.com/search?q=gsl_sf_complex_cos_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Hfwrapper for int gsl_sf_complex_logsin_e(double zr,double zi,gsl_sf_result* lszr,gsl_sf_result* lszi);  ohttp://www.google.com/search?q=gsl_sf_complex_logsin_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ?wrapper for int gsl_sf_sinc_e(double x,gsl_sf_result* result);  ehttp://www.google.com/search?q=gsl_sf_sinc_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky *wrapper for double gsl_sf_sinc(double x);  chttp://www.google.com/search?q=gsl_sf_sinc&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Awrapper for int gsl_sf_lnsinh_e(double x,gsl_sf_result* result);  ghttp://www.google.com/search?q=gsl_sf_lnsinh_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ,wrapper for double gsl_sf_lnsinh(double x);  ehttp://www.google.com/search?q=gsl_sf_lnsinh&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Awrapper for int gsl_sf_lncosh_e(double x,gsl_sf_result* result);  ghttp://www.google.com/search?q=gsl_sf_lncosh_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ,wrapper for double gsl_sf_lncosh(double x);  ehttp://www.google.com/search?q=gsl_sf_lncosh&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky I_wrapper for int gsl_sf_polar_to_rect(double r,double theta,gsl_sf_result* x,gsl_sf_result* y);  lhttp://www.google.com/search?q=gsl_sf_polar_to_rect&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky J_wrapper for int gsl_sf_rect_to_polar(double x,double y,gsl_sf_result* r,gsl_sf_result* theta);  lhttp://www.google.com/search?q=gsl_sf_rect_to_polar&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Lwrapper for int gsl_sf_sin_err_e(double x,double dx,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_sin_err_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Lwrapper for int gsl_sf_cos_err_e(double x,double dx,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_cos_err_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky K=wrapper for int gsl_sf_angle_restrict_symm_e(double* theta);  thttp://www.google.com/search?q=gsl_sf_angle_restrict_symm_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky =wrapper for double gsl_sf_angle_restrict_symm(double theta);  rhttp://www.google.com/search?q=gsl_sf_angle_restrict_symm&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky L<wrapper for int gsl_sf_angle_restrict_pos_e(double* theta);  shttp://www.google.com/search?q=gsl_sf_angle_restrict_pos_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky <wrapper for double gsl_sf_angle_restrict_pos(double theta);  qhttp://www.google.com/search?q=gsl_sf_angle_restrict_pos&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Vwrapper for int gsl_sf_angle_restrict_symm_err_e(double theta,gsl_sf_result* result);  xhttp://www.google.com/search?q=gsl_sf_angle_restrict_symm_err_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky Uwrapper for int gsl_sf_angle_restrict_pos_err_e(double theta,gsl_sf_result* result);  whttp://www.google.com/search?q=gsl_sf_angle_restrict_pos_err_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky    #uses ffi provisional!Alberto Ruiz (aruiz at um dot es)MNOPQRSTUVWXYZ@wrapper for int gsl_sf_zeta_int_e(int n,gsl_sf_result* result);  ihttp://www.google.com/search?q=gsl_sf_zeta_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  +wrapper for double gsl_sf_zeta_int(int n);  ghttp://www.google.com/search?q=gsl_sf_zeta_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky !?wrapper for int gsl_sf_zeta_e(double s,gsl_sf_result* result);  ehttp://www.google.com/search?q=gsl_sf_zeta_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky "*wrapper for double gsl_sf_zeta(double s);  chttp://www.google.com/search?q=gsl_sf_zeta&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky #Awrapper for int gsl_sf_zetam1_e(double s,gsl_sf_result* result);  ghttp://www.google.com/search?q=gsl_sf_zetam1_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky $,wrapper for double gsl_sf_zetam1(double s);  ehttp://www.google.com/search?q=gsl_sf_zetam1&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky %Bwrapper for int gsl_sf_zetam1_int_e(int s,gsl_sf_result* result);  khttp://www.google.com/search?q=gsl_sf_zetam1_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky &-wrapper for double gsl_sf_zetam1_int(int s);  ihttp://www.google.com/search?q=gsl_sf_zetam1_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky 'Iwrapper for int gsl_sf_hzeta_e(double s,double q,gsl_sf_result* result);  fhttp://www.google.com/search?q=gsl_sf_hzeta_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky (4wrapper for double gsl_sf_hzeta(double s,double q);  dhttp://www.google.com/search?q=gsl_sf_hzeta&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky )?wrapper for int gsl_sf_eta_int_e(int n,gsl_sf_result* result);  hhttp://www.google.com/search?q=gsl_sf_eta_int_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky **wrapper for double gsl_sf_eta_int(int n);  fhttp://www.google.com/search?q=gsl_sf_eta_int&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky +>wrapper for int gsl_sf_eta_e(double s,gsl_sf_result* result);  dhttp://www.google.com/search?q=gsl_sf_eta_e&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky ,)wrapper for double gsl_sf_eta(double s);  bhttp://www.google.com/search?q=gsl_sf_eta&as_sitesearch=www.gnu.org/software/gsl/manual&btnI=Lucky  !"#$%&'()*+, !"#$%&'()*+, !"#$%&'()*+,5uses ffi provisional!Alberto Ruiz (aruiz at um dot es)      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,$portable provisionalAlberto Ruiz <aruiz@um.es> -2Creates a StorableArray indexed from 0 to dim -1. T (Memory is efficiently copied, so you can then freely modify the obtained array) .'Creates a Vector from a StorableArray. ` (Memory is efficiently copied, so posterior changes in the array will not affect the result) [\/Ccreates an immutable Array from an hmatrix Vector (to do: unboxed) 0@creates a mutable array from an hmatrix Vector (to do: unboxed) 12bcreates a mutable Array from an hmatrix Vector for manipulation with runSTUArray (to do: unboxed) 3456 -./0123456 /102-.4356 -./0123456portable provisionalAlberto Ruiz <aruiz@um.es> !))! portable provisionalAlberto Ruiz <aruiz@um.es>74Creates a real vector containing a range of values: > linspace 5 (-3,7) 5 |> [-3.0,-0.5,2.0,4.5,7.0]89:;<:creates a vector with a given number of equal components: > constant 2 7 !7 |> [2.0,2.0,2.0,2.0,2.0,2.0,2.0] 789:;<  <789:;789:;<portable provisionalAlberto Ruiz <aruiz@um.es>]2creates a matrix from a vertical list of matrices ^4creates a matrix from a horizontal list of matrices =CCreates a matrix from blocks given as a list of lists of matrices: > let a = @ $   [5,7,2] > let b = * 4 $ < (-1) 12 > fromBlocks [[a,b],[b,a]] (6><7) , [ 5.0, 0.0, 0.0, -1.0, -1.0, -1.0, -1.0 , , 0.0, 7.0, 0.0, -1.0, -1.0, -1.0, -1.0 , , 0.0, 0.0, 2.0, -1.0, -1.0, -1.0, -1.0 , , -1.0, -1.0, -1.0, -1.0, 5.0, 0.0, 0.0 , , -1.0, -1.0, -1.0, -1.0, 0.0, 7.0, 0.0 , , -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, 2.0 ]>Reverse rows ?Reverse columns @/Creates a square matrix with a given diagonal. A&creates a rectangular diagonal matrix /> diagRect (constant 5 3) 3 4 :: Matrix Double (3><4)  [ 5.0, 0.0, 0.0, 0.0  , 0.0, 5.0, 0.0, 0.0  , 0.0, 0.0, 5.0, 0.0 ]B0extracts the diagonal from a rectangular matrix C/creates the identity matrix of given dimension D An easy way to create a matrix: > (2><3)[1..6] (2><3)  [ 1.0, 2.0, 3.0  , 4.0, 5.0, 6.0 ]GThis is the format produced by the instances of Show (Matrix a), which can also be used for input. 7The input list is explicitly truncated, so that it can Csafely be used with lists that are too long (like infinite lists).  Example: > (2>|<3)[1..] (2><3)  [ 1.0, 2.0, 3.0  , 4.0, 5.0, 6.0 ]E9Creates a matrix with the first n rows of another matrix F4Creates a copy of a matrix without the first n rows G<Creates a matrix with the first n columns of another matrix H7Creates a copy of a matrix without the first n columns I Creates a , from a list of lists (considered as rows). > fromLists [[1,2],[3,4],[5,6]] (3><2)  [ 1.0, 2.0  , 3.0, 4.0  , 5.0, 6.0 ]J%creates a 1-row matrix from a vector K(creates a 1-column matrix from a vector L_MZCreates a string from a matrix given a separator and a function to show each entry. Using Gthis function the user can easily define any desired display function: import Text.Printf(printf)disp = putStrLn . format " " (printf "%.2f")N<reads a matrix from a string containing a table of numbers. O=obtains the number of rows and columns in an ASCII data file  (provisionally using unix's wc). P,loads a matrix from a formatted ASCII file. QUrearranges the rows of a matrix according to the order given in a list of integers. RLcreates matrix by repetition of a matrix a given number of rows and columns (> repmat (ident 2) 2 3 :: Matrix Double (4><6)  [ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0  , 0.0, 1.0, 0.0, 1.0, 0.0, 1.0  , 1.0, 0.0, 1.0, 0.0, 1.0, 0.0  , 0.0, 1.0, 0.0, 1.0, 0.0, 1.0 ]'"#$%&'(*+,-.=>?@ABCDEFGHIJKLMNOPQR+D*"I#(JK$%&'=R>?-EFGHQC@AB+,MP.ONL=>?@ABCDEFGHIJKLMNOPQR%uses ffi provisional!Alberto Ruiz (aruiz at um dot es) `aSTUVWXYZ[_"Minimization without derivatives. .desired precision of the solution (size test) %maximum number of iterations allowed  sizes of the initial search box function to minimize starting point &solution vector and optimization path `Minimization with derivatives. 2desired precision of the solution (gradient test) %maximum number of iterations allowed size of the first trial step (tol (precise meaning depends on method) function to minimize  gradient starting point &solution vector and optimization path STUVWXYZ[\]^_`_Y[Z`SXWVUT\]^ SXWVUTTUVWXY[ZZ[_`&uses ffi provisional!Alberto Ruiz (aruiz at um dot es)bcabcdefghijkNNonlinear multidimensional root finding using algorithms that do not require 8 any derivative information to be supplied by the user. @ Any derivatives needed are approximated by finite differences. maximum residual %maximum number of iterations allowed function to minimize starting point &solution vector and optimization path lUNonlinear multidimensional root finding using both the function and its derivatives. maximum residual %maximum number of iterations allowed function to minimize  Jacobian starting point &solution vector and optimization path abcdefghijkl kfjihglaedcb aedcbbcdefjihgghijkl'uses -fffi and -fglasgow-exts provisional!Alberto Ruiz (aruiz at um dot es)mVThis action removes the GSL default error handler (which aborts the program), so that N GSL errors can be handled by Haskell (using Control.Exception) and ghci doesn' t abort. defghijklFyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,STUVWXYZ[\]^_`abcdefghijklmmm(uses ffi provisional!Alberto Ruiz (aruiz at um dot es)nconversion utilities opqrstmQconverts a real vector into a complex representation (with zero imaginary parts) MdefghijklF "#$%&'(*+,-.789:;<=>?@ABCDEFGHIJKLMNOPQRnopqrstnopqrstnopqrstopqrst)uses ffi provisional!Alberto Ruiz (aruiz at um dot es) ujA generic interface for vectors and matrices to a few element-by-element functions in Numeric.GSL.Vector. vwxyz"element by element multiplication {element by element division |7scale the element by element reciprocal of the object: scaleRecip 2 (fromList [5,i]#) == 2 |> [0.4 :+ 0.0,0.0 :+ (-2.0)] } uvwxyz{|} uvwxyz{|} uvwxyz{|}vwxyz{|}6portable provisional!Alberto Ruiz (aruiz at um dot es)no*portable (uses FFI) provisional!Alberto Ruiz (aruiz at um dot es)9pqrstuvwxyz{|}~~Matrix product based on BLAS's dgemm. Matrix product based on BLAS's zgemm. Wrapper for LAPACK's dgesvd>, which computes the full svd decomposition of a real matrix. (u,s,v)=full svdR m so that m=u <> s <>  v. Wrapper for LAPACK's dgesvd>, which computes the full svd decomposition of a real matrix. (u,s,v)=full svdRdd m so that m=u <> s <>  v. Wrapper for LAPACK's zgesvdA, which computes the full svd decomposition of a complex matrix. (u,s,v)=full svdC m so that m=u <> comp s <>  v. Wrapper for LAPACK's zgeevU, which computes the eigenvalues and right eigenvectors of a general complex matrix: if  (l,v)=eigC m then m <> v = v <> diag l. 'The eigenvectors are the columns of v. ! The eigenvalues are not sorted. Wrapper for LAPACK's dgeevR, which computes the eigenvalues and right eigenvectors of a general real matrix: if  (l,v)=eigR m then m <> v = v <> diag l. 'The eigenvectors are the columns of v. ! The eigenvalues are not sorted. Wrapper for LAPACK's dsyevT, which computes the eigenvalues and right eigenvectors of a symmetric real matrix: if  (l,v)=eigSl m then m <> v = v <> diag l. 'The eigenvectors are the columns of v. 9 The eigenvalues are sorted in descending order (use eigS' for ascending order). Wrapper for LAPACK's zheevW, which computes the eigenvalues and right eigenvectors of a hermitian complex matrix: if  (l,v)=eigH m then m <> s v = v <> diag l. 'The eigenvectors are the columns of v. 9 The eigenvalues are sorted in descending order (use eigH' for ascending order). Wrapper for LAPACK's dgesvr, which solves a general real linear system (for several right-hand sides) internally using the lu decomposition. Wrapper for LAPACK's zgesvu, which solves a general complex linear system (for several right-hand sides) internally using the lu decomposition. Wrapper for LAPACK's dgels, which obtains the least squared error solution of an overconstrained real linear system or the minimum norm solution of an underdetermined system, for several right-hand sides. For rank deficient systems use . Wrapper for LAPACK's zgels, which obtains the least squared error solution of an overconstrained complex linear system or the minimum norm solution of an underdetermined system, for several right-hand sides. For rank deficient systems use . Wrapper for LAPACK's dgelss, which obtains the minimum norm solution to a real linear least squares problem Ax=B using the svd, for several right-hand sides. Admits rank deficient systems but it is slower than . The effective rank of A is determined by treating as zero those singular valures which are less than rcond times the largest singular value. If rcond == Nothing machine precision is used. rcond coefficient matrix right hand sides (as columns) solution vectors (as columns) Wrapper for LAPACK's zgelss, which obtains the minimum norm solution to a complex linear least squares problem Ax=B using the svd, for several right-hand sides. Admits rank deficient systems but it is slower than . The effective rank of A is determined by treating as zero those singular valures which are less than rcond times the largest singular value. If rcond == Nothing machine precision is used. rcond coefficient matrix right hand sides (as columns) solution vectors (as columns) Wrapper for LAPACK's zpotrf1, which computes the Cholesky factorization of a - complex Hermitian positive definite matrix. Wrapper for LAPACK's dpotrf1, which computes the Cholesky factorization of a * real symmetric positive definite matrix. Wrapper for LAPACK's dgeqr26, which computes a QR factorization of a real matrix. Wrapper for LAPACK's zgeqr29, which computes a QR factorization of a complex matrix. Wrapper for LAPACK's dgehrdE, which computes a Hessenberg factorization of a square real matrix. Wrapper for LAPACK's zgehrdH, which computes a Hessenberg factorization of a square complex matrix. Wrapper for LAPACK's dgees@, which computes a Schur factorization of a square real matrix. Wrapper for LAPACK's zgeesC, which computes a Schur factorization of a square complex matrix. Wrapper for LAPACK's dgetrf>, which computes a LU factorization of a general real matrix. Wrapper for LAPACK's zgeesC, which computes a Schur factorization of a square complex matrix. Wrapper for LAPACK's dgetrsp, which solves a general real linear system (for several right-hand sides) from a precomputed LU decomposition. Wrapper for LAPACK's zgetrsp, which solves a general real linear system (for several right-hand sides) from a precomputed LU decomposition. ~~~+uses ffi provisional!Alberto Ruiz (aruiz at um dot es)>Objects which have a p-norm. / Using it you can define convenient shortcuts: norm2 x = pnorm PNorm2 x!frobenius m = norm2 . flatten $ m\Auxiliary typeclass used to define generic computations for both real and complex matrices. )Singular value decomposition using lapack's dgesvd or zgesvd. RObtains the LU decomposition of a matrix in a compact data structure suitable for . aSolution of a linear system (for several right hand sides) from the precomputed LU factorization  obtained by . PSolution of a general linear system (for several right-hand sides) using lapacks' dgesv or zgesv.  It is similar to  . , but  linearSolve1 raises an error if called on a singular system. , See also other versions of linearSolve in Numeric.LinearAlgebra.LAPACK. DEigenvalues and eigenvectors of a general square matrix using lapack's dgeev or zgeev. If  (s,v) = eig m then m < > v == v <> diag s  Similar to C without checking that the input matrix is hermitian or symmetric.  Similar to C without checking that the input matrix is hermitian or symmetric. QR factorization using lapack's dgeqr2 or zgeqr2. If  (q,r) = qr m then m == q <> r0, where q is unitary and r is upper triangular. %Hessenberg factorization using lapack's dgehrd or zgehrd. If (p,h) = hess m then m == p <> h < > ctrans p, where p is unitary $ and h is in upper Hessenberg form.  Schur factorization using lapack's dgees or zgees. If (u,s) = schur m then m == u <> s < > ctrans u, where u is unitary \ and s is a Shur matrix. A complex Schur matrix is upper triangular. A real Schur matrix is ! upper triangular in 2x2 blocks. "GAnything that the Jordan decomposition can do, the Schur decomposition  can do better!" (Van Loan) Generic conjugate transpose. Matrix product. YEigenvalues and Eigenvectors of a complex hermitian or real symmetric matrix using lapack's dsyev or zheev. If (s,v) = eigSH m then m == v < > diag s < > ctrans v XCholesky factorization of a positive definite hermitian or symmetric matrix using lapack's dpotrf or zportrf. If  c = chol m then m == ctrans c <> c. Ddeterminant of a square matrix, computed from the LU decomposition. :Explicit LU factorization of a general matrix using lapack's dgetrf or zgetrf. If (l,u,p,s) = lu m then m == p <> l <> u, where l is lower triangular, ] u is upper triangular, p is a permutation matrix and s is the signature of the permutation. (Inverse of a square matrix using lapacks' dgesv and zgesv. .Pseudoinverse of a general matrix using lapack's dgelss or zgelss.  A version of H which returns an appropriate diagonal matrix with the singular values. If (u,d,v) = full svd m then m == u <> d < > trans v.  A version of i which returns only the nonzero singular values and the corresponding rows and columns of the rotations. If (u,s,v) = economy svd m then m == u < > diag s < > trans v. #The machine precision of a Double: eps = 2.22044604925031e-16! (the value used by GNU-Octave). The imaginary unit: i = 0.0 :+ 1.0 6The nullspace of a matrix from its SVD decomposition. relative tolerance in  units  input matrix /list of unitary vectors spanning the nullspace _The nullspace of a matrix, assumed to be one-dimensional, with default tolerance (shortcut for last . nullspacePrec 1). NReciprocal of the 2-norm condition number of a matrix, computed from the SVD. 0Number of linearly independent rows or columns. DGeneric matrix functions for diagonalizable matrices. For instance: logm = matFunc logNMatrix exponential. It uses a direct translation of Algorithm 11.3.1 in Golub & Van Loan, + based on a scaled Pade approximation. [Matrix square root. Currently it uses a simple iterative algorithm described in Wikipedia. jIt only works with invertible matrices that have a real solution. For diagonalizable matrices you can try  matFunc sqrt. m = (2><2) [4,9  ,0,4] :: Matrix Double>sqrtm m (2><2)  [ 2.0, 2.25  , 0.0, 2.0 ]Euclidean inner product. Outer product of two vectors. >   [1,2,3] `outer`   [5,2,3] (3><3)  [ 5.0, 2.0, 3.0  , 10.0, 4.0, 6.0  , 15.0, 6.0, 9.0 ]#Kronecker product of two matrices. m1=(2><3)  [ 1.0, 2.0, 0.0  , 0.0, -1.0, 3.0 ] m2=(4><3)  [ 1.0, 2.0, 3.0  , 4.0, 5.0, 6.0  , 7.0, 8.0, 9.0  , 10.0, 11.0, 12.0 ]> kronecker m1 m2 (8><9) ; [ 1.0, 2.0, 3.0, 2.0, 4.0, 6.0, 0.0, 0.0, 0.0 ; , 4.0, 5.0, 6.0, 8.0, 10.0, 12.0, 0.0, 0.0, 0.0 ; , 7.0, 8.0, 9.0, 14.0, 16.0, 18.0, 0.0, 0.0, 0.0 ; , 10.0, 11.0, 12.0, 20.0, 22.0, 24.0, 0.0, 0.0, 0.0 ; , 0.0, 0.0, 0.0, -1.0, -2.0, -3.0, 3.0, 6.0, 9.0 ; , 0.0, 0.0, 0.0, -4.0, -5.0, -6.0, 12.0, 15.0, 18.0 ; , 0.0, 0.0, 0.0, -7.0, -8.0, -9.0, 21.0, 24.0, 27.0 ; , 0.0, 0.0, 0.0, -10.0, -11.0, -12.0, 30.0, 33.0, 36.0 ],,+,portable provisional!Alberto Ruiz (aruiz at um dot es) matrix product u <.> v = dot u vx .* a = scale x aa */ x = scale (recip x) a:least squares solution of a linear system, similar to the \ operator of Matlab/"Octave (based on linearSolveSVD). 2Horizontal concatenation of matrices and vectors:  > (ident 3 <-> 3 * ident 3) <|> fromList [1..6.0] (6><4)  [ 1.0, 0.0, 0.0, 1.0  , 0.0, 1.0, 0.0, 2.0  , 0.0, 0.0, 1.0, 3.0  , 3.0, 0.0, 0.0, 4.0  , 0.0, 3.0, 0.0, 5.0  , 0.0, 0.0, 3.0, 6.0 ]0Vertical concatenation of matrices and vectors. 7uses ffi provisional!Alberto Ruiz (aruiz at um dot es)defghijklF "#$%&'(*+,-.789:;<=>?@ABCDEFGHIJKLMNOPQRnopqrstuvwxyz{|}8portable provisional!Alberto Ruiz (aruiz at um dot es) 9portable provisional!Alberto Ruiz (aruiz at um dot es) -portable provisional!Alberto Ruiz (aruiz at um dot es)9All tests must pass with a maximum dimension of about 20 A (some tests may fail with bigger sizes due to precision loss). maximum dimension .uses gnuplot and ImageMagick provisional!Alberto Ruiz (aruiz at um dot es) 6Loads a real matrix from a formatted ASCII text file "fromFile :: FilePath -> IO Matrix CfromFile filename = readFile filename >>= return . readMatrix read 3Saves a real matrix to a formatted ascii text file lFrom vectors x and y, it generates a pair of matrices to be used as x and y arguments for matrix functions. 4Draws a 3D surface representation of a real matrix.  > mesh (hilb 20) NIn certain versions you can interactively rotate the graphic using the mouse. mDraws the surface represented by the function f in the desired ranges and number of points, internally using .  > let f x y = cos (x + y) " > splot f (0,pi) (0,2*pi) 50 -plots several vectors against the first one TDraws a list of functions over a desired range and with a desired number of points + > plot [sin, cos, sin.(3*)] (0,2*pi) 1000 SDraws a parametric curve. For instance, to draw a spiral we can do something like: > > parametricPlot (\t->(t * sin t, t * cos t)) (0,10*pi) 1000 "writes a matrix to pgm image file Qimshow shows a representation of a matrix as a gray level image using ImageMagick' s display.   /:/;/</=/>0?0@0A0B0C0D0E0F0G0H0I0J0K0L0M0N0O1P1Q1R1S1T1U1V1W1X1Y1Z1[1\1]1^1_1`1a1b1c1d1e1f1g1hijklmnopqrstuvwxyz{|}~ 4444                                  ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 56789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456 7 8 9 : ; < = > ? @ A B!C!D!E!F"G"H"I"J"K"L"M"N"O"P"Q"R"S"T"U"V"W"X#Y#Z#[#\#]#^#_#`#a#b#c#d#e#f$g$h$i$j$k$l$m$n$o$pqrstuvwxyz{|}~%%%%%%%%%%%%%%&&&&&&&&&&&&'((((((()))))))))*****************************++++++++++++++++++++O++++++++++++++++++++++++,,,,,,,--.. . . . . ..../////////////// /!/"/#/$/%/&/'/(/)/*/+/,/-/.///0/1/2/3/4/5/6/7/8/9/:/;/</=/>/?/@0A0B0C0D0E0F0G0H0I0J0K1L1M1N1O1P1Q1R1S1T1U1V1W1X1Y1Z1[1\1111]1^1_1`1a1b1c1d1e1fghijklmnopqrstuvrwxyz{|} ~ 33333333444444444                                                                                                                                                 ! " # $ % & ' ( ) * +,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOP Q R S T U V W X Y Z [ \ ] ^!_!`!a!b"c"d"e"f"g"h"i"j"k"l"m"n"o"p"q"r"s"t"u"v"w"x"y"z"{"|"}"~""""##############$$%%&&xyxyxyxyxyxyxyxyxy(66******************************+++++++++++++++++++,,,,t88888888888888888888888888888888888999999999999999999999 9 9 9 9 99999999--.hmatrix-0.5.2.0Data.Packed.DevelopmentData.Packed.VectorData.Packed.MatrixNumeric.GSL.VectorData.Packed.STNumeric.GSL.DifferentiationNumeric.GSL.IntegrationNumeric.GSL.FourierNumeric.GSL.PolynomialsNumeric.GSL.Special.AiryNumeric.GSL.Special.BesselNumeric.GSL.Special.ClausenNumeric.GSL.Special.CoulombNumeric.GSL.Special.CouplingNumeric.GSL.Special.DawsonNumeric.GSL.Special.DebyeNumeric.GSL.Special.DilogNumeric.GSL.Special.ElementaryNumeric.GSL.Special.EllintNumeric.GSL.Special.ErfNumeric.GSL.Special.ExpNumeric.GSL.Special.ExpintNumeric.GSL.Special.Fermi_diracNumeric.GSL.Special.GammaNumeric.GSL.Special.GegenbauerNumeric.GSL.Special.HypergNumeric.GSL.Special.LaguerreNumeric.GSL.Special.LambertNumeric.GSL.Special.LegendreNumeric.GSL.Special.LogNumeric.GSL.Special.Pow_intNumeric.GSL.Special.PsiNumeric.GSL.Special.SynchrotronNumeric.GSL.Special.TrigNumeric.GSL.Special.ZetaData.Packed.ConvertNumeric.GSL.MinimizationNumeric.GSL.Root Numeric.GSL Data.PackedNumeric.LinearAlgebra.LinearNumeric.LinearAlgebra.LAPACK Numeric.LinearAlgebra.AlgorithmsNumeric.LinearAlgebra.InterfaceNumeric.LinearAlgebra.Tests Graphics.PlotData.Packed.Internal.CommonData.Packed.Internal.VectorData.Packed.Internal.MatrixData.Packed.InternalNumeric.GSL.InternalNumeric.GSL.Special.InternalNumeric.GSL.SpecialNumeric.LinearAlgebra.InstancesNumeric.LinearAlgebra%Numeric.LinearAlgebra.Tests.Instances&Numeric.LinearAlgebra.Tests.PropertiesAdaptapp1app2app3app4Vectordimvec createVectorfromListtoList|> subVector@>join liftVector liftVector2 mapVector zipVector foldVectorfoldLoop foldVectorGElementMatrixrowscols MatrixOrder ColumnMajorRowMajororderOftranscmatfmatmatflattentoListsfromRowstoRows fromColumns toColumns@@> createMatrixreshape liftMatrix liftMatrix2 subMatrixfromFileFunCodeSMinMinIdxMaxMaxIdxAbsSumNorm2 FunCodeVVATan2PowDivMulSubAdd FunCodeSVPowVSPowSVNegate AddConstantRecipScaleFunCodeVSqrtSignLogExpATanhACoshASinhTanhCoshSinhATanACosASinAbsTanCosSin 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exprel_n_eexprel_n exprel_n_CF_e exp_err_e exp_err_e10_eexp_mult_err_eexp_mult_err_e10_e expint_E1_e expint_E1 expint_E2_e expint_E2 expint_En_e expint_Enexpint_E1_scaled_eexpint_E1_scaledexpint_E2_scaled_eexpint_E2_scaledexpint_En_scaled_eexpint_En_scaled expint_Ei_e expint_Eiexpint_Ei_scaled_eexpint_Ei_scaledshi_eshichi_echi expint_3_eexpint_3si_esici_eci atanint_eatanintfermi_dirac_m1_efermi_dirac_m1fermi_dirac_0_e fermi_dirac_0fermi_dirac_1_e fermi_dirac_1fermi_dirac_2_e fermi_dirac_2fermi_dirac_int_efermi_dirac_intfermi_dirac_mhalf_efermi_dirac_mhalffermi_dirac_half_efermi_dirac_halffermi_dirac_3half_efermi_dirac_3halffermi_dirac_inc_0_efermi_dirac_inc_0 lngamma_elngammagamma_egamma gammastar_e gammastar gammainv_egammainv taylorcoeff_e taylorcoefffact_efact doublefact_e doublefactlnfact_elnfactlndoublefact_e lndoublefact lnchoose_elnchoosechoose_echooselnpoch_elnpochpoch_epoch pochrel_epochrel gamma_inc_Q_e gamma_inc_Q gamma_inc_P_e gamma_inc_P gamma_inc_e 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Gsl_sf_resultSFSize_t Gsl_mode_tprecCode createSFR createSFR_E10gsl_sf_airy_zero_Bi_derivgsl_sf_airy_zero_Bi_deriv_egsl_sf_airy_zero_Ai_derivgsl_sf_airy_zero_Ai_deriv_egsl_sf_airy_zero_Bigsl_sf_airy_zero_Bi_egsl_sf_airy_zero_Aigsl_sf_airy_zero_Ai_egsl_sf_airy_Bi_deriv_scaledgsl_sf_airy_Bi_deriv_scaled_egsl_sf_airy_Ai_deriv_scaledgsl_sf_airy_Ai_deriv_scaled_egsl_sf_airy_Bi_derivgsl_sf_airy_Bi_deriv_egsl_sf_airy_Ai_derivgsl_sf_airy_Ai_deriv_egsl_sf_airy_Bi_scaledgsl_sf_airy_Bi_scaled_egsl_sf_airy_Ai_scaledgsl_sf_airy_Ai_scaled_egsl_sf_airy_Bigsl_sf_airy_Bi_egsl_sf_airy_Aigsl_sf_airy_Ai_egsl_sf_bessel_zero_Jnugsl_sf_bessel_zero_Jnu_egsl_sf_bessel_zero_J1gsl_sf_bessel_zero_J1_egsl_sf_bessel_zero_J0gsl_sf_bessel_zero_J0_egsl_sf_bessel_lnKnugsl_sf_bessel_lnKnu_egsl_sf_bessel_Knugsl_sf_bessel_Knu_egsl_sf_bessel_Knu_scaledgsl_sf_bessel_Knu_scaled_egsl_sf_bessel_Inugsl_sf_bessel_Inu_egsl_sf_bessel_Inu_scaledgsl_sf_bessel_Inu_scaled_egsl_sf_bessel_sequence_Jnu_egsl_sf_bessel_Ynugsl_sf_bessel_Ynu_egsl_sf_bessel_Jnugsl_sf_bessel_Jnu_egsl_sf_bessel_kl_scaled_arraygsl_sf_bessel_kl_scaledgsl_sf_bessel_kl_scaled_egsl_sf_bessel_k2_scaledgsl_sf_bessel_k2_scaled_egsl_sf_bessel_k1_scaledgsl_sf_bessel_k1_scaled_egsl_sf_bessel_k0_scaledgsl_sf_bessel_k0_scaled_egsl_sf_bessel_il_scaled_arraygsl_sf_bessel_il_scaledgsl_sf_bessel_il_scaled_egsl_sf_bessel_i2_scaledgsl_sf_bessel_i2_scaled_egsl_sf_bessel_i1_scaledgsl_sf_bessel_i1_scaled_egsl_sf_bessel_i0_scaledgsl_sf_bessel_i0_scaled_egsl_sf_bessel_yl_arraygsl_sf_bessel_ylgsl_sf_bessel_yl_egsl_sf_bessel_y2gsl_sf_bessel_y2_egsl_sf_bessel_y1gsl_sf_bessel_y1_egsl_sf_bessel_y0gsl_sf_bessel_y0_egsl_sf_bessel_jl_steed_arraygsl_sf_bessel_jl_arraygsl_sf_bessel_jlgsl_sf_bessel_jl_egsl_sf_bessel_j2gsl_sf_bessel_j2_egsl_sf_bessel_j1gsl_sf_bessel_j1_egsl_sf_bessel_j0gsl_sf_bessel_j0_egsl_sf_bessel_Kn_scaled_arraygsl_sf_bessel_Kn_scaledgsl_sf_bessel_Kn_scaled_egsl_sf_bessel_K1_scaledgsl_sf_bessel_K1_scaled_egsl_sf_bessel_K0_scaledgsl_sf_bessel_K0_scaled_egsl_sf_bessel_Kn_arraygsl_sf_bessel_Kngsl_sf_bessel_Kn_egsl_sf_bessel_K1gsl_sf_bessel_K1_egsl_sf_bessel_K0gsl_sf_bessel_K0_egsl_sf_bessel_In_scaled_arraygsl_sf_bessel_In_scaledgsl_sf_bessel_In_scaled_egsl_sf_bessel_I1_scaledgsl_sf_bessel_I1_scaled_egsl_sf_bessel_I0_scaledgsl_sf_bessel_I0_scaled_egsl_sf_bessel_In_arraygsl_sf_bessel_Ingsl_sf_bessel_In_egsl_sf_bessel_I1gsl_sf_bessel_I1_egsl_sf_bessel_I0gsl_sf_bessel_I0_egsl_sf_bessel_Yn_arraygsl_sf_bessel_Yngsl_sf_bessel_Yn_egsl_sf_bessel_Y1gsl_sf_bessel_Y1_egsl_sf_bessel_Y0gsl_sf_bessel_Y0_egsl_sf_bessel_Jn_arraygsl_sf_bessel_Jngsl_sf_bessel_Jn_egsl_sf_bessel_J1gsl_sf_bessel_J1_egsl_sf_bessel_J0gsl_sf_bessel_J0_ebessel_Jn_arraybessel_Yn_arraybessel_In_arraybessel_In_scaled_arraybessel_Kn_arraybessel_Kn_scaled_arraybessel_jl_arraybessel_jl_steed_arraybessel_yl_arraybessel_il_scaled_arraybessel_kl_scaled_arraybessel_sequence_Jnu_egsl_sf_clausengsl_sf_clausen_egsl_sf_coulomb_CL_arraygsl_sf_coulomb_CL_egsl_sf_coulomb_wave_sphF_arraygsl_sf_coulomb_wave_FGp_arraygsl_sf_coulomb_wave_FG_arraygsl_sf_coulomb_wave_F_arraygsl_sf_coulomb_wave_FG_egsl_sf_hydrogenicRgsl_sf_hydrogenicR_egsl_sf_hydrogenicR_1gsl_sf_hydrogenicR_1_ecoulomb_wave_FG_ecoulomb_wave_F_arraycoulomb_wave_FG_arraycoulomb_wave_FGp_arraycoulomb_wave_sphF_arraycoulomb_CL_arraygsl_sf_coupling_6j_INCORRECTgsl_sf_coupling_6j_INCORRECT_egsl_sf_coupling_9jgsl_sf_coupling_9j_egsl_sf_coupling_RacahWgsl_sf_coupling_RacahW_egsl_sf_coupling_6jgsl_sf_coupling_6j_egsl_sf_coupling_3jgsl_sf_coupling_3j_ecoupling_6j_INCORRECT_ecoupling_6j_INCORRECT gsl_sf_dawsongsl_sf_dawson_egsl_sf_debye_6gsl_sf_debye_6_egsl_sf_debye_5gsl_sf_debye_5_egsl_sf_debye_4gsl_sf_debye_4_egsl_sf_debye_3gsl_sf_debye_3_egsl_sf_debye_2gsl_sf_debye_2_egsl_sf_debye_1gsl_sf_debye_1_egsl_sf_complex_spence_xy_egsl_sf_complex_dilog_egsl_sf_complex_dilog_xy_e gsl_sf_diloggsl_sf_dilog_ecomplex_dilog_xy_ecomplex_dilog_ecomplex_spence_xy_egsl_sf_multiply_err_egsl_sf_multiplygsl_sf_multiply_egsl_sf_ellint_RJgsl_sf_ellint_RJ_egsl_sf_ellint_RFgsl_sf_ellint_RF_egsl_sf_ellint_RDgsl_sf_ellint_RD_egsl_sf_ellint_RCgsl_sf_ellint_RC_egsl_sf_ellint_Dgsl_sf_ellint_D_egsl_sf_ellint_Pgsl_sf_ellint_P_egsl_sf_ellint_Egsl_sf_ellint_E_egsl_sf_ellint_Fgsl_sf_ellint_F_egsl_sf_ellint_Dcompgsl_sf_ellint_Dcomp_egsl_sf_ellint_Pcompgsl_sf_ellint_Pcomp_egsl_sf_ellint_Ecompgsl_sf_ellint_Ecomp_egsl_sf_ellint_Kcompgsl_sf_ellint_Kcomp_e gsl_sf_hazardgsl_sf_hazard_e gsl_sf_erf_Q gsl_sf_erf_Zgsl_sf_erf_Q_egsl_sf_erf_Z_e gsl_sf_erf gsl_sf_erf_egsl_sf_log_erfcgsl_sf_log_erfc_e gsl_sf_erfc 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gsl_sf_poch gsl_sf_poch_egsl_sf_lnpoch_sgn_e gsl_sf_lnpochgsl_sf_lnpoch_e gsl_sf_choosegsl_sf_choose_egsl_sf_lnchoosegsl_sf_lnchoose_egsl_sf_lndoublefactgsl_sf_lndoublefact_e gsl_sf_lnfactgsl_sf_lnfact_egsl_sf_doublefactgsl_sf_doublefact_e gsl_sf_fact gsl_sf_fact_egsl_sf_taylorcoeffgsl_sf_taylorcoeff_egsl_sf_lngamma_complex_egsl_sf_gammainvgsl_sf_gammainv_egsl_sf_gammastargsl_sf_gammastar_e gsl_sf_gammagsl_sf_gamma_egsl_sf_lngamma_sgn_egsl_sf_lngammagsl_sf_lngamma_e lngamma_sgn_elngamma_complex_e lnpoch_sgn_e lnbeta_sgn_egsl_sf_gegenpoly_arraygsl_sf_gegenpoly_ngsl_sf_gegenpoly_n_egsl_sf_gegenpoly_3gsl_sf_gegenpoly_2gsl_sf_gegenpoly_1gsl_sf_gegenpoly_3_egsl_sf_gegenpoly_2_egsl_sf_gegenpoly_1_egegenpoly_arraygsl_sf_hyperg_2F0gsl_sf_hyperg_2F0_egsl_sf_hyperg_2F1_conj_renormgsl_sf_hyperg_2F1_conj_renorm_egsl_sf_hyperg_2F1_renormgsl_sf_hyperg_2F1_renorm_egsl_sf_hyperg_2F1_conjgsl_sf_hyperg_2F1_conj_egsl_sf_hyperg_2F1gsl_sf_hyperg_2F1_egsl_sf_hyperg_U_e10_egsl_sf_hyperg_Ugsl_sf_hyperg_U_egsl_sf_hyperg_U_int_e10_egsl_sf_hyperg_U_intgsl_sf_hyperg_U_int_egsl_sf_hyperg_1F1gsl_sf_hyperg_1F1_egsl_sf_hyperg_1F1_intgsl_sf_hyperg_1F1_int_egsl_sf_hyperg_0F1gsl_sf_hyperg_0F1_egsl_sf_laguerre_ngsl_sf_laguerre_n_egsl_sf_laguerre_3gsl_sf_laguerre_2gsl_sf_laguerre_1gsl_sf_laguerre_3_egsl_sf_laguerre_2_egsl_sf_laguerre_1_egsl_sf_lambert_Wm1gsl_sf_lambert_Wm1_egsl_sf_lambert_W0gsl_sf_lambert_W0_egsl_sf_legendre_H3d_arraygsl_sf_legendre_H3dgsl_sf_legendre_H3d_egsl_sf_legendre_H3d_1gsl_sf_legendre_H3d_1_egsl_sf_legendre_H3d_0gsl_sf_legendre_H3d_0_egsl_sf_conicalP_cyl_reggsl_sf_conicalP_cyl_reg_egsl_sf_conicalP_sph_reggsl_sf_conicalP_sph_reg_egsl_sf_conicalP_1gsl_sf_conicalP_1_egsl_sf_conicalP_0gsl_sf_conicalP_0_egsl_sf_conicalP_mhalfgsl_sf_conicalP_mhalf_egsl_sf_conicalP_halfgsl_sf_conicalP_half_egsl_sf_legendre_array_size"gsl_sf_legendre_sphPlm_deriv_arraygsl_sf_legendre_sphPlm_arraygsl_sf_legendre_sphPlmgsl_sf_legendre_sphPlm_egsl_sf_legendre_Plm_deriv_arraygsl_sf_legendre_Plm_arraygsl_sf_legendre_Plmgsl_sf_legendre_Plm_egsl_sf_legendre_Qlgsl_sf_legendre_Ql_egsl_sf_legendre_Q1gsl_sf_legendre_Q1_egsl_sf_legendre_Q0gsl_sf_legendre_Q0_egsl_sf_legendre_P3gsl_sf_legendre_P2gsl_sf_legendre_P1gsl_sf_legendre_P3_egsl_sf_legendre_P2_egsl_sf_legendre_P1_egsl_sf_legendre_Pl_deriv_arraygsl_sf_legendre_Pl_arraygsl_sf_legendre_Plgsl_sf_legendre_Pl_elegendre_Pl_arraylegendre_Pl_deriv_arraylegendre_Plm_arraylegendre_Plm_deriv_arraylegendre_sphPlm_arraylegendre_sphPlm_deriv_arraylegendre_H3d_arraygsl_sf_log_1plusx_mxgsl_sf_log_1plusx_mx_egsl_sf_log_1plusxgsl_sf_log_1plusx_egsl_sf_complex_log_egsl_sf_log_absgsl_sf_log_abs_e 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