ERCIM News No.46, July 2001 [contents]

Updating Abramowitz & Stegun

by Nico Temme

A project is underway at the US National Institute of Standards and Technology (NIST) to develop a replacement for the Handbook of Mathematical Functions, commonly known as ‘Abramowitz & Stegun’, after its principal editors. This will be a major new mathematical reference source on the World Wide Web for special functions and their applications.

The Handbook, published in 1964 by the National Bureau of Standards, is probably the most widely-used book on special functions, and perhaps even in mathematics at large. This book, whose sales number in the hundreds of thousands, may well be the most frequently cited source of all mathematical reference works. A paperback version has been photo-offset and sold by Dover Publications since 1965. Although Dover does not reveal sales data, it undoubtedly outsells the government edition many times over.

The Handbook has never been revised, although there have been numerous advances in basic theory, computational methods, and domains of application since its publication. Its structure is that of a static reference volume; though still very useful, it does not meet the needs of modern users for information that can be conveniently exploited in a highly computer-oriented technical environment. Such needs have been communicated regularly to NIST (formerly, National Bureau of Standards). About five years ago it was decided at NIST that a successor to the NBS Handbook should be designed in the form of a knowledge base, called the Digital Library of Mathematical Functions (DLMF). Via free access over the World Wide Web, using standard Web browsers, individuals will be able to obtain validated mathematical information in a semantic-based representation that incorporates metadata, interactive features, and extensive linkages. The Web server will be constructed, maintained and operated by NIST. The many tables in the existing version of the Handbook will not be present in the new version. They are inadequate to current needs, particularly when used to validate numerical software. Second, software packages exist that can compute vastly extended numerical tables. New chapters will be:

CWI is involved in this project. Nico Temme, a specialist on Asymptotics and Special Functions, is a member of the Editorial Board, and will write several chapters (on exponential integrals, error functions and parabolic cylinder functions). The Executive Committee for the whole project consists of the four Principal Editors: Daniel W. Lozier, Frank W. J. Olver, Charles W. Clark, and Ronald F. Boisvert. The Board of Associate Editors: R. A. Askey, M. V. Berry, W.Gautschi, L. C. Maximon, M. Newman, I. Olkin, P. Paule, Johannes Kepler, W. P. Reinhardt, N. M. Temme, and J. Wimp. The project is expected to be completed by 2003.


Please contact:
Nico Temme — CWI
Tel: +31 20 592 4240