''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 Milton Abramowitz (19 February 1915 in Brooklyn, New York – 5 July 1958) was a Jewish American mathematician at the National Bureau of Standards who, with Irene Stegun, edited a classic book of mathematical tables called '' Handbook of Mathemati ...

and

Irene Stegun Irene Ann Stegun (February 9, 1919 – January 27, 2008) was an American mathematician at the National Bureau of Standards (NBS, now the National Institute of Standards and Technology) who edited a classic book of mathematical tables called ''A ...

of the United States

National Bureau of Standards 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 physical sci ...

(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 The Digital Library of Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology (NIST) to develop a database of mathematical reference data for special functions and their applications. It is inte ...

" (DLMF) on 11 May 2010, along with a printed version, the ''

NIST Handbook of Mathematical Functions The Digital Library of Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology (NIST) to develop a database of mathematical reference data for special functions and their applications. It is intend ...

'', published by

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Pre ...

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 defined b ...

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 mathemati ...

. 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 la ...

'' 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 A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The d ...

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". 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 information ...

, 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, book ...

(), 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 run Print circulation is the average number of copies of a publication. The number of copies of a non-periodical publication (such as a book) are usually called print run. Circulation is not always the same as copies sold, often called paid circulat ...

s including a growing number of corrections. Original NBS edition: * 1st printing: June 1964;

errata An erratum or corrigendum (plurals: errata, corrigenda) (comes from la, errata corrige) is a correction of a published text. As a general rule, publishers issue an erratum for a production error (i.e., an error introduced during the publishing pro ...

: * 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

: * 1st printing: 1965 * ? * 9th printing with additional corrections (based on 10th printing of NBS edition with corrections)

Related projects

Michael Danos and

Johann Rafelski Johann Rafelski (born 19 May 1950) is a German-American theoretical physicist. He is professor of Physics at The University of Arizona in Tucson, guest scientist at CERN ( Geneva), and has been LMU-Excellent Guest Professor at the Ludwig Maxi ...

edited the ''Pocketbook of Mathematical Functions'', published by

Verlag Harri Deutsch The (VHD, HD) with headquarters in Frankfurt am Main, Germany, as well as in Zürich and Thun, Switzerland, was a German publishing house founded in 1961 and closed in 2013. Overview The ' with headquarters in Frankfurt am Main, Germany, w ...

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 calculators. 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 “

” (DLMF) on 11 May 2010, along with a printed version, the ''

'', published by

Notes

References

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