Author | Milton Abramowitz and Irene Stegun |
---|---|
Language | English |
Genre | Math |
Publisher | United States Department of Commerce, National Bureau of Standards (NBS) |
Publication date | 1964 |
Publication place | United States |
ISBN | 0-486-61272-4 |
OCLC | 18003605 |
Abramowitz and Stegun (AS) is the informal name of a 1964 mathematical reference work 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. [1]
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. [2] [3] [4] 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".
More than 1,000 pages long, the Handbook of Mathematical Functions was first published in 1964 and reprinted many times, with yet another reprint in 1999. Its influence on science and engineering is evidenced by its popularity. In fact, when New Scientist magazine recently asked some of the world's leading scientists what single book they would want if stranded on a desert island, one distinguished British physicist [5] said he would take the Handbook. The Handbook is likely the most widely distributed and most cited NIST technical publication of all time. Government sales exceed 150,000 copies, and an estimated three times as many have been reprinted and sold by commercial publishers since 1965. During the mid-1990s, the book was cited every 1.5 hours of each working day. And its influence will persist as it is currently being updated in digital format by NIST.
The chapters are:
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, it has also been reprinted by commercial publishers, most notably Dover Publications ( ISBN 0-486-61272-4), 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:
Reprint edition by Dover Publications:
Michael Danos and Johann Rafelski edited the Pocketbook of Mathematical Functions, published by Verlag Harri Deutsch in 1984. [14] [15] 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, [14] which, by this time, could be easily calculated with scientific pocket calculators. [15] The references were removed as well. [15] Most known errata were incorporated, the physical constants updated and the now-first chapter saw some slight enlargement compared to the former second chapter. [15] The numbering of formulas was kept for easier cross-reference. [15]
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. [1]
In mathematics, the family of Debye functions is defined by
In mathematics, the Legendre forms of elliptic integrals are a canonical set of three elliptic integrals to which all others may be reduced. Legendre chose the name elliptic integrals because the second kind gives the arc length of an ellipse of unit semi-major axis and eccentricity .
The Mathematical Tables Project was one of the largest and most sophisticated computing organizations that operated prior to the invention of the digital electronic computer. Begun in the United States in 1938 as a project of the Works Progress Administration (WPA), it employed 450 unemployed clerks to tabulate higher mathematical functions, such as exponential functions, logarithms, and trigonometric functions. These tables were eventually published in a 28-volume set by Columbia University Press.
Milton Abramowitz 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 Mathematical Functions, widely known as Abramowitz and Stegun. Abramowitz died of a heart attack in 1958, at which time the book was not yet completed but was well underway. Stegun took over management of the project and was able to finish the work by 1964, working under the direction of the NBS Chief of Numerical Analysis Philip J. Davis, who was also a contributor to the book.
Handbook of Mathematical Functions may refer to:
In mathematics, and in particular the study of Weierstrass elliptic functions, the equianharmonic case occurs when the Weierstrass invariants satisfy g2 = 0 and g3 = 1. This page follows the terminology of Abramowitz and Stegun; see also the lemniscatic case.
In mathematics, Gegenbauer polynomials or ultraspherical polynomialsC(α)
n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer.
In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration. Series acceleration techniques may also be used, for example, to obtain a variety of identities on special functions. Thus, the Euler transform applied to the hypergeometric series gives some of the classic, well-known hypergeometric series identities.
Irene Ann Stegun was an American mathematician at the National Bureau of Standards who edited a classic book of mathematical tables called A Handbook of Mathematical Functions, widely known as Abramowitz and Stegun.
There are a number of notational systems for the Jacobi theta functions. The notations given in the Wikipedia article define the original function
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 intended as an update of Abramowitz's and Stegun's Handbook of Mathematical Functions (A&S). It was published online on 7 May 2010, though some chapters appeared earlier. In the same year it appeared at Cambridge University Press under the title NIST Handbook of Mathematical Functions.
In mathematics, the Jacobi–Anger expansion is an expansion of exponentials of trigonometric functions in the basis of their harmonics. It is useful in physics, and in signal processing. This identity is named after the 19th-century mathematicians Carl Jacobi and Carl Theodor Anger.
Lucy Joan Slater was a mathematician who worked on hypergeometric functions, and who found many generalizations of the Rogers–Ramanujan identities.
The Sievert integral, named after Swedish medical physicist Rolf Sievert, is a special function commonly encountered in radiation transport calculations.
In mathematics, Boole's rule, named after George Boole, is a method of numerical integration.
In mathematics, the Jacobi zeta functionZ(u) is the logarithmic derivative of the Jacobi theta function Θ(u). It is also commonly denoted as
In statistics, the Cunningham function or Pearson–Cunningham function ωm,n(x) is a generalisation of a special function introduced by Pearson (1906) and studied in the form here by Cunningham (1908). It can be defined in terms of the confluent hypergeometric function U, by
In mathematics, Einstein function is a name occasionally used for one of the functions
In mathematics, the Neville theta functions, named after Eric Harold Neville, are defined as follows:
Gradshteyn and Ryzhik (GR) is the informal name of a comprehensive table of integrals originally compiled by the Russian mathematicians I. S. Gradshteyn and I. M. Ryzhik. Its full title today is Table of Integrals, Series, and Products.