Abramowitz and Stegun
Encyclopedia
Abramowitz and Stegun is the informal name of a mathematical
reference work edited by Milton Abramowitz
and Irene Stegun
of the U.S.
National Bureau of Standards (now the National Institute of Standards and Technology). Its full title is Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.
Since it was first published in 1964, the 1046 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 system
s 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".
employees acting in their official capacity, it is not protected by copyright. While it can be ordered from the Government Printing Office, it has also been reprinted by commercial publishers, most notably Dover Publications
(ISBN 0-486-61272-4), and can be legally viewed and downloaded off the web.
” (DLMF) on May 11, 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press
.(ISBN 978-0-521-19225-5). More information can be found at NIST.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
reference work edited by Milton Abramowitz
Milton Abramowitz
Milton Abramowitz was a mathematician at the National Bureau of Standards who, with Irene Stegun, edited a classic book of mathematical tables called Handbook of Mathematical Functions, widely known as Abramowitz and Stegun. Abramowitz died of a heart attack in 1958, at which time the book was not...
and Irene Stegun
Irene Stegun
Irene Anne Stegun was a mathematician at the National Bureau of Standards who, with Milton Abramowitz, edited a classic book of mathematical tables called A Handbook of Mathematical Functions, widely known as Abramowitz and Stegun...
of the U.S.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
National Bureau of Standards (now the National Institute of Standards and Technology). Its full title is Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.
Since it was first published in 1964, the 1046 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
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
. The notation used in the Handbook is the de facto
De facto
De facto is a Latin expression that means "concerning fact." In law, it often means "in practice but not necessarily ordained by law" or "in practice or actuality, but not officially established." It is commonly used in contrast to de jure when referring to matters of law, governance, or...
standard for much of applied mathematics today.
At the time of its publication, the Handbook was an essential resource for practitioners. Nowadays, computer algebra system
Computer algebra system
A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...
s have replaced the function tables
Mathematical table
Before calculators were cheap and plentiful, people would use mathematical tables —lists of numbers showing the results of calculation with varying arguments— to simplify and drastically speed up computation...
, 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".
Editions
Because the Handbook is the work of U.S. federal governmentFederal government of the United States
The federal government of the United States is the national government of the constitutional republic of fifty states that is the United States of America. The federal government comprises three distinct branches of government: a legislative, an executive and a judiciary. These branches and...
employees acting in their official capacity, it is not protected by copyright. While it can be ordered from the Government Printing Office, it has also been reprinted by commercial publishers, most notably Dover Publications
Dover Publications
Dover Publications is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche. It publishes primarily reissues, books no longer published by their original publishers. These are often, but not always, books in the public domain. The original published editions may be...
(ISBN 0-486-61272-4), and can be legally viewed and downloaded off the web.
Successor
A digital successor to the Handbook, long under development at NIST, was released as the “Digital library of mathematical functionsDigital Library of Mathematical Functions
The Digital Library of Mathematical Functions is an online project at the National Institute of Standards and Technology to develop a major resource of mathematical reference data for special functions and their applications. It is intended as an update of Abramowitz's and Stegun's Handbook of...
” (DLMF) on May 11, 2010, along with a printed version, the NIST Handbook of Mathematical Functions, published by Cambridge University Press
Cambridge University Press
Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
.(ISBN 978-0-521-19225-5). More information can be found at NIST.
See also
- Numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
- Philip J. DavisPhilip J. DavisPhilip J. Davis is an American applied mathematician.Davis was born in Lawrence, Massachusetts. He is known for his work in numerical analysis and approximation theory, as well as his investigations in the history and philosophy of mathematics...
, author of the Gamma functionGamma functionIn mathematics, the gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers...
section and other sections of the book - Digital Library of Mathematical FunctionsDigital Library of Mathematical FunctionsThe Digital Library of Mathematical Functions is an online project at the National Institute of Standards and Technology to develop a major resource of mathematical reference data for special functions and their applications. It is intended as an update of Abramowitz's and Stegun's Handbook of...
(DLMF), from the National Institute of Standards and TechnologyNational Institute of Standards and TechnologyThe National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...
(NIST), is intended to be a replacement for Abramowitz and Stegun's Handbook of Mathematical Functions - Boole's ruleBoole's ruleIn mathematics, Boole's rule, named after George Boole, is a method of numerical integration. It approximates an integralby using the values of ƒ at five equally spaced pointsIt is expressed thus Abramowitz and Stegun :...
, a mathematical rule of integration sometimes known as Bode's rule, due to a typo in Abramowitz and Stegun (1972, p. 886) that was subsequently propagated
External links
- How to order the book from GPO.
- A high quality scan of the book, in PDF and TIFF formats, hosted at the University of Birmingham, UK
- The book in scanned format, hosted at Simon Fraser University.
- Another scanned version by ConvertIt.com
- Empanel version
- NIST Digital Library of Mathematical Functions, the digital companion to the Handbook