OPSF

Overview

• Special Funcitons (Wikipedia page)

• Why are Special Functions Special? (by Micheal Berry)

• The History and Future of Special Functions (by Stephen Wolfram, LLC)

Web Resourses

Online Handbooks

• NIST Digital Library of Mathematical Functions (DLMF)

• Handbook of Mathematical Functions (Abramowitz and Stegun)

• The Wolfram Function Site

• Special Functions Wiki

Downloadable Handbooks

• Higher Transcendental Functions [Volumes I-III] (the Bateman Manuscript Project)

• Tables of Integral Transforms [Volumes I & II] (the Bateman Manuscript Project)

Orginaztions

• SIAM Activity Group on Orthogonal Polynomials and Special Functions

Softwares and Packages

Fortran90 packages

• FN

  Gamma function, Beta function, Airy funciton, Bessel function of orders zero and one, confluent hypergeometric function, elliptic integral, Dawson's integral,

• IMSL Numerical Libraries

  Exponential integrals, Gamma function, Error function, Airy function, Bessel function, elliptic integrals, elliptic functions, Mathieu functions

• SpecFun by William Cody and Laura Stoltz.

  Bessel functions of any positive non-integer order, Gamma function, logarithm of the Gamma function, exponential integrals, error function, Psi function, Dawson's integral.

Matlab packages

• Chebfun

  Chebfun is an open-source software system for numerical computing with functions.

Books

Reference Books

• A Course of Modern Analysis (by E. T. Whittaker and G. N. Watson)

• Special Functions and Their Applications(by N. N. Lebedev)

• Special Functions (by Z. X. Guo and D. R. Wang)

• Special Functions (by G. E. Andrews, R. Askey and R. Roy)

• Special Functions and Orthogonal Polynomials (by R. Beals and R. Wong)

• Special Functions: A Unified Theory Based on Singularities (by S. Yu. Slavyanov and W. Lay)

Handbooks and Tables

• Encyclopedia of Special Functions: The Askey-Bateman Project. Vol 1. Univariate Orthogonal Polynomials (ed. by M. E. H. Ismail)

• Encyclopedia of Special Functions: The Askey-Bateman Project, Vol 2. Multivariable Special Functions (ed. by T. H. Koornwinder and J. V. Stokman)

• Table of Integrals, Series, and Products (ed. by Daniel Zwillinger)

• Integrals and Series (by A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev)

  Volume 1: Elementary Functions; Volume 2: Special Functions; Volume 3: More Special Functions; Volume 4: Direct Laplace Transforms; Volume 5: Inverse Laplace Transforms

• Handbook of Special Functions (by Yury A. Brychkov)

  Derivatives, Integral, Serires and Other Formulas