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Encyclopedia > Handbook of Mathematical Functions

Abramowitz and Stegun is the informal moniker of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the U.S. National Bureau of Standards. Its full title is Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.

Since it was first published in 1964, the 1000+ page Handbook has been one of the most comprehensive sources of information on special functions, containing definitions, identities, approximations, plots, and tables of values of numerous functions used in virtually all fields of applied mathematics. The notation used in the Handbook is the de facto standard for much of applied mathematics today.

At the time of its publication, the Handbook was an essential resource for practitioners. Nowadays, computer algebra systems have replaced the function tables, but the Handbook remains an important reference source. (The foreword discusses a meeting in 1954 in which it was agreed that "the advent of high-speed computing equipment changed the task of table making but definitely did not remove the need for tables".)

Because the Handbook is the product of US Government employees acting in official capacity, it is not protected by copyright. While it can be ordered from the Government Printing Office, it has also been reprinted by commerical publishers, most notably Dover Publications (ISBN 0486612724), and can be legally viewed and downloaded off the web (see below for URLs).

BibTeX entry:

 @Book{abramowitz+stegun, author = "Milton Abramowitz and Irene A. Stegun", title = "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables", publisher = "Dover", year = 1964, address = "New York", edition = "ninth Dover printing, tenth GPO printing", isbn = "0-486-61272-4" } 

External links

  • How to order the book from GPO (http://dlmf.nist.gov/about/book_info.php).
  • The book in scanned format, hosted at Simon Fraser University (http://www.math.sfu.ca/~cbm/aands/), ProHosting (http://jove.prohosting.com/~skripty/), ConvertIt (http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=200&Page=0).
  • Annotations by Linas Vepstas (http://linas.org/art-gallery/abramowitz/html/AS-annotions.html).

  Results from FactBites:
A Short History of Mathematical Function Tables (991 words)
Functions describing solutions to these problems were often expressed as infinite series, as integrals, or as solutions to differential equations.
Functions that cropped up most frequently in scientific calculations were given names and notations which have come into common usage: Bessel functions, Struve functions, Mathieu functions, the spherical harmonics, the Gamma function, the Beta function, Jacobi functions, and most of the others appearing on this website.
Parallel to the handbooks dealing with series expansions, differential equations, functional identities, and so forth of special functions, many integral tables were developed in the 20th century.
Physics Today April 2001 (1453 words)
Some of these functions were (with one class of exceptions) known to mathematicians in 1964, but they were not well known to scientists, and had rarely been applied in physics.
Functions of hypergeometric type can be ordered by the behavior of singular points of the differential equations representing them, or by a group-theoretical analysis of their symmetries.
Of the two Airy functions, Ai is the one that decays towards infinity, while Bi grows; the J Bessel functions are regular at the origin, the Y Bessel functions have a pole or a branch point.
  More results at FactBites »



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