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(Specific detailed sources for individual functions and distributions are given at the end of each individual section).
DLMF (NIST Digital Library of Mathematical Functions) is a replacement for the legendary Abramowitz and Stegun's Handbook of Mathematical Functions (often called simply A&S),
M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C.
NIST Handbook of Mathematical Functions Edited by: Frank W. J. Olver, University of Maryland and National Institute of Standards and Technology, Maryland, Daniel W. Lozier, National Institute of Standards and Technology, Maryland, Ronald F. Boisvert, National Institute of Standards and Technology, Maryland, Charles W. Clark, National Institute of Standards and Technology, Maryland and University of Maryland.
ISBN: 978-0521140638 (paperback), 9780521192255 (hardback), July 2010, Cambridge University Press.
NIST/SEMATECH e-Handbook of Statistical Methods
Mathematica Documentation: DiscreteDistributions The Wolfram Research Documentation Center is a collection of online reference materials about Mathematica, CalculationCenter, and other Wolfram Research products.
Mathematica Documentation: ContinuousDistributions The Wolfram Research Documentation Center is a collection of online reference materials about Mathematica, CalculationCenter, and other Wolfram Research products.
Statistical Distributions (Wiley Series in Probability & Statistics) (Paperback) by N.A.J. Hastings, Brian Peacock, Merran Evans, ISBN: 0471371246, Wiley 2000.
Extreme Value Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah, ISBN 978-1-86094-224-2 & 1-86094-224-5 Oct 2000, Chapter 1.2 discusses the various extreme value distributions.
pugh.pdf (application/pdf Object) Pugh Msc Thesis on the Lanczos approximation to the gamma function.
We found (and used to create cross-check spot values - as far as their accuracy allowed).
The Wolfram Functions Site The Wolfram Functions Site - Providing the mathematical and scientific community with the world's largest (and most authoritative) collection of formulas and graphics about mathematical functions.
100-decimal digit calculator provided some spot values.
http://www.adsciengineering.com/bpdcalc/ Binomial Probability Distribution Calculator.
Cephes library by Shephen Moshier and his book:
Methods and programs for mathematical functions, Stephen L B Moshier, Ellis Horwood (1989) ISBN 0745802893 0470216093 provided inspiration.
CDFLIB Library of Fortran Routines for Cumulative Distribution functions.
DCDFLIB C++ version DCDFLIB is a library of C++ routines, using double precision arithmetic, for evaluating cumulative probability density functions.
http://www.softintegration.com/docs/package/chnagstat/
NAG libraries.
JMSL Numerical Library (Java).
John F Hart, Computer Approximations, (1978) ISBN 0 088275 642-7.
William J Cody, Software Manual for the Elementary Functions, Prentice-Hall (1980) ISBN 0138220646.
Nico Temme, Special Functions, An Introduction to the Classical Functions of Mathematical Physics, Wiley, ISBN: 0471-11313-1 (1996) who also gave valuable advice.
Statistics Glossary, Valerie Easton and John H. McColl.
_R R Development Core Team (2010). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
For use of R, see:
Jim Albert, Bayesian Computation with R, ISBN 978-0-387-71384-7.
C++ Statistical Distributions in Boost - QuantNetwork forum discusses using Boost.Math in finance.
Quantnet Boost and computational finance. Robert Demming & Daniel J. Duffy, Introduction to the C++ Boost Libraries - Volume I - Foundations and Volume II ISBN 978-94-91028-01-4, Advanced Libraries and Applications, ISBN 978-94-91028-02-1 (to be published in 2011). discusses application of Boost.Math, especially in finance.