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-- |
-- Module : Numeric.SpecFunctions
-- Copyright : (c) 2009, 2011, 2012 Bryan O'Sullivan
-- License : BSD3
--
-- Maintainer : bos@serpentine.com
-- Stability : experimental
-- Portability : portable
--
-- Special functions and factorials.
module Numeric.SpecFunctions (
-- * Error function
erf
, erfc
, invErf
, invErfc
-- * Gamma function
, logGamma
, logGammaL
, incompleteGamma
, invIncompleteGamma
, digamma
-- * Beta function
, logBeta
, incompleteBeta
, incompleteBeta_
, invIncompleteBeta
-- * Sinc
, sinc
-- * Logarithm
-- $log1p
, log1p
, log1pmx
, log2
-- * Exponent
, expm1
-- * Factorial
, factorial
, logFactorial
, stirlingError
-- * Combinatorics
, choose
, logChoose
-- * References
-- $references
) where
import Numeric.SpecFunctions.Internal
-- $log1p
--
-- Base starting from @4.9.0@ (GHC 8.0) provides 'log1p' and 'expm1'
-- as method of class 'Floating'. In this case we simply reexport
-- these function. Otherwise we provide our own with more restrictive
-- signature @Double → Double@.
-- $references
--
-- * Bernardo, J. (1976) Algorithm AS 103: Psi (digamma)
-- function. /Journal of the Royal Statistical Society. Series C
-- (Applied Statistics)/ 25(3):315-317.
-- <http://www.jstor.org/stable/2347257>
--
-- * Cran, G.W., Martin, K.J., Thomas, G.E. (1977) Remark AS R19
-- and Algorithm AS 109: A Remark on Algorithms: AS 63: The
-- Incomplete Beta Integral AS 64: Inverse of the Incomplete Beta
-- Function Ratio. /Journal of the Royal Statistical Society. Series
-- C (Applied Statistics)/ Vol. 26, No. 1 (1977), pp. 111-114
-- <http://www.jstor.org/pss/2346887>
--
-- * Lanczos, C. (1964) A precision approximation of the gamma
-- function. /SIAM Journal on Numerical Analysis B/
-- 1:86–96. <http://www.jstor.org/stable/2949767>
--
-- * Loader, C. (2000) Fast and Accurate Computation of Binomial
-- Probabilities. <http://projects.scipy.org/scipy/raw-attachment/ticket/620/loader2000Fast.pdf>
--
-- * Macleod, A.J. (1989) Algorithm AS 245: A robust and reliable
-- algorithm for the logarithm of the gamma function.
-- /Journal of the Royal Statistical Society, Series C (Applied Statistics)/
-- 38(2):397–402. <http://www.jstor.org/stable/2348078>
--
-- * Majumder, K.L., Bhattacharjee, G.P. (1973) Algorithm AS 63: The
-- Incomplete Beta Integral. /Journal of the Royal Statistical
-- Society. Series C (Applied Statistics)/ Vol. 22, No. 3 (1973),
-- pp. 409-411. <http://www.jstor.org/pss/2346797>
--
-- * Majumder, K.L., Bhattacharjee, G.P. (1973) Algorithm AS 64:
-- Inverse of the Incomplete Beta Function Ratio. /Journal of the
-- Royal Statistical Society. Series C (Applied Statistics)/
-- Vol. 22, No. 3 (1973), pp. 411-414
-- <http://www.jstor.org/pss/2346798>
--
-- * Temme, N.M. (1992) Asymptotic inversion of the incomplete beta
-- function. /Journal of Computational and Applied Mathematics
-- 41(1992) 145-157.
--
-- * Temme, N.M. (1994) A set of algorithms for the incomplete gamma
-- functions. /Probability in the Engineering and Informational
-- Sciences/, 8, 1994, 291-307. Printed in the U.S.A.
|
