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''Abramowitz and Stegun'' (''AS'') is the informal name of a 1964 mathematical
reference work A reference work is a work, such as a paper, book or periodical (or their electronic equivalents), to which one can refer for information. The information is intended to be found quickly when needed. Such works are usually ''referred'' to ...
edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the ''National Institute of Standards and Technology'' (NIST). Its full title is ''Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables''. A digital successor to the Handbook was released as the " Digital Library of Mathematical Functions" (DLMF) on 11 May 2010, along with a printed version, the '' NIST Handbook of Mathematical Functions'', published by
Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambr ...
.


Overview

Since it was first published in 1964, the 1046 page ''Handbook'' has been one of the most comprehensive sources of information on
special function Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defin ...
s, containing definitions, identities, approximations, plots, and tables of values of numerous functions used in virtually all fields of
applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemat ...
. The notation used in the ''Handbook'' is the ''
de facto ''De facto'' ( ; , "in fact") describes practices that exist in reality, whether or not they are officially recognized by laws or other formal norms. It is commonly used to refer to what happens in practice, in contrast with '' de jure'' ("by l ...
'' 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". The chapters are: # Mathematical Constants # Physical Constants and Conversion Factors # Elementary Analytical Methods # Elementary Transcendental Functions # Exponential Integral and Related Functions # Gamma Function and Related Functions # Error Function and Fresnel Integrals # Legendre Functions # Bessel Functions of Integral Order # Bessel Functions of Fractional Order # Integrals of Bessel Functions # Struve Functions and Related Functions # Confluent Hypergeometric Functions # Coulomb Wave Functions # Hypergeometric Functions # Jacobian Elliptic Functions and Theta Functions # Elliptic Integrals # Weierstrass Elliptic and Related Functions # Parabolic Cylinder Functions # Mathieu Functions # Spheroidal Wave Functions # Orthogonal Polynomials # Bernoulli and Euler Polynomials, Riemann Zeta Function # Combinatorial Analysis # Numerical Interpolation, Differentiation, and Integration # Probability Functions # Miscellaneous Functions # Scales of Notation # Laplace Transforms


Editions

Because the ''Handbook'' is the work of U.S. federal government employees acting in their official capacity, it is not protected by copyright in the United States. While it could be ordered from the
Government Printing Office The United States Government Publishing Office (USGPO or GPO; formerly the United States Government Printing Office) is an agency of the legislative branch of the United States Federal government. The office produces and distributes informati ...
, it has also been reprinted by commercial publishers, most notably
Dover Publications Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, books ...
(), and can be legally viewed on and downloaded from the web. While there was only one edition of the work, it went through many print runs including a growing number of corrections. Original NBS edition: * 1st printing: June 1964; errata: * 2nd printing with corrections: November 1964; errata: * 3rd printing with corrections: March 1965; errata: * 4th printing with corrections: December 1965; errata: * 5th printing with corrections: August 1966 * 6th printing with corrections: November 1967 * 7th printing with corrections: May 1968 * 8th printing with corrections: 1969 * 9th printing with corrections: November 1970 * 10th printing with corrections: December 1972 Reprint edition by
Dover Publications Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, books ...
: * 1st printing: 1965 * ? * 9th printing with additional corrections (based on 10th printing of NBS edition with corrections)


Related projects

Michael Danos and Johann Rafelski edited the ''Pocketbook of Mathematical Functions'', published by Verlag Harri Deutsch in 1984. The book is an abridged version of Abramowitz's and Stegun's Handbook, retaining most of the formulas (except for the first and the two last original chapters, which were dropped), but reducing the numerical tables to a minimum, which, by this time, could be easily calculated with
scientific pocket calculator A scientific calculator is an electronic calculator, either desktop or handheld, designed to perform mathematical operations. They have completely replaced slide rules and are used in both educational and professional settings. In some are ...
s. The references were removed as well. Most known errata were incorporated, the physical constants updated and the now-first chapter saw some slight enlargement compared to the former second chapter. The numbering of formulas was kept for easier cross-reference. A digital successor to the Handbook, long under development at NIST, was released as the “ Digital Library of Mathematical Functions” (DLMF) on 11 May 2010, along with a printed version, the '' NIST Handbook of Mathematical Functions'', published by
Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambr ...
.


See also

* Mathematical Tables Project, a 1938–1948
Works Progress Administration The Works Progress Administration (WPA; renamed in 1939 as the Work Projects Administration) was an American New Deal agency that employed millions of jobseekers (mostly men who were not formally educated) to carry out public works projects, in ...
(WPA) project to calculate mathematical tables, including those later used in Abramowitz and Stegun's Handbook of Mathematical Functions *
Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...
* Rubber book, a ''Handbook of Chemistry & Physics'' * Reference book * Handbook * MAOL, a Finnish handbook for science *
BINAS The Binas (Often written as BiNaS or BINAS) is a Dutch science reference work (a '' handbook'') for the higher levels of secondary school, consisting largely of tables and formulas. The name stands for biologie, natuurkunde, scheikunde (biology ...
, a Dutch science handbook * Philip J. Davis, author of the
Gamma function In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except th ...
section and other sections of the book * Louis Melville Milne-Thomson, author of the book chapters on elliptic integrals and Jacobi elliptic functions * Digital Library of Mathematical Functions (DLMF), from the
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into Outline of p ...
(NIST), is intended to be a replacement for Abramowitz and Stegun's Handbook of Mathematical Functions * Boole's rule, 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.


Notes


References


Further reading

* * (NB. A history of the activities leading up to and surrounding the development of the Handbook.)


External links

* A high quality scan of the book, in PDF and TIFF formats, hosted a
the University of Birmingham, UK
* The book in scanned format, now hosted a
the University of British Columbia, CA
(formerly at Simon Fraser University). # but this scan dropped tables of numbers. For example, the pages contained table of abscissas and weights of Gauss quadrature formulas are omitted. Only formulas are scanned.
Another scanned version
by ConvertIt.com
numerical.recipes
download - NBS, Tenth Printing, December 1972, with Corrections - PDF without Search
NIST Digital Library of Mathematical Functions
the digital successor of the Handbook {{Authority control 1964 non-fiction books Handbooks and manuals Mathematics books Mathematical tables Numerical analysis Reference works in the public domain Special functions