-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Hypergeometric functions
--   
--   Haskell implementation of hypergeometric functions and associated
--   statistical and special functions: erf, normal cdf, incomplete beta,
--   regularized beta, F-distribution cdf, <math>-distribution cdf,
--   t-distrubtion cdf. Also includes Lanczos' approximation of the gamma
--   function.
@package hypergeometric
@version 0.1.5.0


-- | See Shaw, Ewart <a>"Hypergeometric Functions and CDFs in J"</a>.
module Math.Hypergeometric

-- | &lt;math&gt;
--   
--   The radius of convergence is
--   
--   &lt;math&gt;
--   
--   This iterates until the result stabilizes.
hypergeometric :: (Ord a, Fractional a) => [a] -> [a] -> a -> a

-- | Euler's transform:
--   
--   &lt;math&gt;
--   
--   The right-hand side converges for all &lt;math&gt;.
--   
--   Koekoek, Roelef and Swarttouw, René F. <a>The Askey-scheme of
--   hypergeometric orthogonal polynomials and its q-analogue</a>.
euler :: (Ord a, Floating a) => a -> a -> a -> a -> a

-- | <a>erf</a>
erf :: (Ord a, Floating a) => a -> a

-- | CDF of the standard normal &lt;math&gt;
ncdf :: (Ord a, Floating a) => a -> a

module Math.SpecialFunction

-- | Incomplete beta function, &lt;math&gt;
--   
--   Calculated with &lt;math&gt;
incbeta :: (Floating a, Ord a) => a -> a -> a -> a

-- | &lt;math&gt;
--   
--   This uses <a>gammaln</a> under the hood to extend its domain somewhat.
beta :: (Floating a, Ord a) => a -> a -> a

-- | <a>Regularized beta function</a>, &lt;math&gt;
--   
--   &lt;math&gt;
regbeta :: (Floating a, Ord a) => a -> a -> a -> a

-- | Bessel functions of the first kind, &lt;math&gt;.
bessel1 :: (Floating a, Ord a) => a -> a -> a

-- | &lt;math&gt;
gamma :: (Floating a, Ord a) => a -> a

-- | &lt;math&gt;
--   
--   Lanczos approximation. This is exactly the approach described in
--   Press, William H. et al. <i>Numerical Recipes</i>, 3rd ed., extended
--   to work on negative real numbers.
gammaln :: (Floating a, Ord a) => a -> a

-- | <a>Arithmetic-geometric mean</a>
agm :: (Ord a, Floating a) => a -> a -> a

-- | <a>Complete elliptic integral of the first kind</a>
completeElliptic :: (Ord a, Floating a) => a -> a

fcdf :: (Floating a, Ord a) => a -> a -> a -> a

chisqcdf :: (Floating a, Ord a) => a -> a -> a

-- | Converges if and only if &lt;math&gt;
tcdf :: (Floating a, Ord a) => a -> a -> a