NIST Digital Library of Mathematical Functions

Together with Tom H. Koornwinder, Roderick S.C. Wong and René F. Swarttouw I have written a chapter on Orthogonal Polynomials for the Digital Library of Mathematical Functions (DLMF). This project was organized by the Mathematics Department of the National Institute of Standards and Technology (NIST).

Starting point of the project was to review and update the Handbook of Mathematical Functions (with Formulas, Graphs, and Mathematical Tables) edited by M. Abramowitz and I.A. Stegun. An online version of this book can be found here or here. This handbook was first published by the National Bureau of Standards (NBS) in 1964 and last corrected in 1972. It is still in print. This National Bureau of Standards (NBS) was renamed the National Institute of Standards and Technology (NIST) in 1988.

Final goal of the project was to make the Digital Library of Mathematical Functions (DLMF) an electronic publication on the World Wide Web. It should turn out to be a major new mathematical reference source on the World Wide Web for special functions and their applications.

See also the articles "A new testament for special functions?" by Barry A. Cipra in SIAM News, Volume 31, Number 2, March 1998 and "Why are special functions special?" by Michael Berry in Physics Today, Volume 54, Number 4, April 2001.

The website of the DLMF can be found here:

Digital Library of Mathematical Functions (DLMF)

It will also appear in printed form published by Cambridge University Press:

NIST Handbook of Mathematical Functions


ISBN 978-0-521-19225-5 (Hardback)

ISBN 978-0-521-14063-8 (Paperback)

Last modified on March 2, 2010

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  • Hypergeometric Orthogonal Polynomials and Their q-Analogues Hypergeometric Orthogonal Polynomials and Their q-Analogues
  • Classification of hypergeometric orthogonal polynomials Classification of hypergeometric orthogonal polynomials
  • NIST Digital Library of Mathematical Functions NIST Digital Library of Mathematical Functions
  • The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
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