úÎ6m4¸     8Evaluate a Chebyshev polynomial of the first kind. Uses  Clenshaw' s algorithm. Parameter of each function. ;Coefficients of each polynomial term, in increasing order. ?Evaluate a Chebyshev polynomial of the first kind. Uses Broucke's F ECHEB algorithm, and his convention for coefficient handling, and so  gives different results than  for the same inputs. Parameter of each function. ;Coefficients of each polynomial term, in increasing order. ,Compute the logarithm of the gamma function “(x ). Uses  Algorithm AS 245 by Macleod. Gives an accuracy of 10 &12 significant decimal digits, except  for small regions around x = 1 and x = 2, where the function * goes to zero. For greater accuracy, use . Returns ") if the input is outside of the range (0 < x  "d 1e305). -Compute the logarithm of the gamma function, “(x ). Uses a  Lanczos approximation. This function is slower than , but gives 14 or more 7 significant decimal digits of accuracy, except around x = 1 and  x' = 2, where the function goes to zero. Returns ") if the input is outside of the range (0 < x  "d 1e305). ,Compute the log gamma correction factor for x "e 10. This : correction factor is suitable for an alternate (but less % numerically accurate) definition of : Elgg x = 0.5 * log(2*pi) + (x-0.5) * log x - x + logGammaCorrection x 7Compute the normalized lower incomplete gamma function  ³(s,x). Normalization means that  ³(s,"$)=1. Uses Algorithm AS 239 by Shea. s x %Inverse incomplete gamma function. It's approximately inverse of   for the same s. So following equality  approximately holds:  / invIncompleteGamma s . incompleteGamma s = id For invIncompleteGamma s p s must be positive and p must be  in [0,1] range. 4Compute the natural logarithm of the beta function. =Regularized incomplete beta function. Uses algorithm AS63 by  Majumder abd Bhattachrjee. p > 0 q > 0 x, must lie in [0,1] range .Regularized incomplete beta function. Same as  9 but also takes logarithm of beta function as parameter. logarithm of beta function p > 0 q > 0 x, must lie in [0,1] range  >Compute inverse of regularized incomplete beta function. Uses G initial approximation from AS109 and Halley method to solve equation. p q a  %Compute the natural logarithm of 1 + x. This is accurate even  for values of x near zero, where use of log(1+x) would lose  precision. O(log n)5 Compute the logarithm in base 2 of the given value. Compute the factorial function n !. Returns " if the E input is above 170 (above which the result cannot be represented by  a 64-bit ). @Compute the natural logarithm of the factorial function. Gives ! 16 decimal digits of precision. )Quickly compute the natural logarithm of n  k, with  no checking. !Compute the binomial coefficient n `` k. For  values of k2 > 30, this uses an approximation for performance E reasons. The approximation is accurate to 12 decimal places in the  worst case  Example:  7 `choose` 3 == 35  sqrt 2  sqrt (2 * pi) The smallest  µ such that 1 + µ "` 1.  log(sqrt((2*pi))Positive infinity. Negative infinity. Not a number.      !      !"#math-functions-0.1.0.0Numeric.Polynomial.ChebyshevNumeric.SpecFunctions chebyshevchebyshevBrouckelogGamma logGammaLincompleteGammainvIncompleteGammalogBetaincompleteBetaincompleteBeta_invIncompleteBetalog1plog2 factorial logFactorialchooseBCLlogGammaCorrectionincompleteBetaWorkerinvIncompleteBetaWorkerghc-prim GHC.TypesDouble logChooseFastm_sqrt_2 m_sqrt_2_pi m_epsilonm_ln_sqrt_2_pi m_pos_inf m_neg_infm_NaN