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Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
2014 Reprint of 1964 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Despite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of automatic computers, however, and because of recent scientific advances, a greater variety of functions and a higher accuracy of tabulation than have been available until now are required. In 1954, a conference on mathematical tables, sponsored by M.I.T. and the National Science Foundation, met to discuss a modernization and extension of Jahnke and Emde's classical tables of functions. This volume, published 10 years later by the U.S. Department of Commerce, is the result. Designed to include a maximum of information and to meet the needs of scientists in all fields, it is a monumental piece of work, a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems. The book contains 29 sets of tables, some to as high as 20 places: mathematical constants; physical constants and conversion factors (6 tables); exponential integral and related functions (7); error function and Fresnel integrals (12); Bessel functions of integer (12) and fractional (13) order; integrals of Bessel functions (2); Struve and related functions (2); confluent hypergeometric functions (2); Coulomb wave functions (2); hypergeometric functions; Jacobian elliptic and theta functions (2); elliptic integrals {9); Weierstrass elliptic and related functions; parabolic cylinder functions {3); Mathieu functions (2); spheroidal wave functions (5); orthogonal polynomials (13); combinatorial analysis (9); numerical interpolation, differentiation and integration (11); probability functions (ll); scales of notation {6); miscellaneous functions {9); Laplace transforms (2); and others. Each of these sections is prefaced by a list of related formulas and graphs: differential equations, series expansions, special functions, and other basic relations. These constitute an unusually valuable reference work in themselves. The prefatory material also includes an explanation of the numerical methods involved in using the tables that follow and a bibliography. Numerical examples illustrate the use of each table and explain the computation of function values which lie outside its range, while the editors' introduction describes higher-order interpolation procedures. Well over 100 figures illustrate the text. In all, this is one of the most ambitious and useful books of its type ever published, an essential aid in all scientific and engineering research, problem solving, experimentation and field work. This low-cost edition contains every page of the original government publication. Preface by A. V. Astin. Foreword by Advisory Committee, Conference on Mathematical Tables. Editors' Introduction. Indices to Subjects, Notations.
1064 pages, Paperback
First published June 1, 1965
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Displaying 1 - 4 of 4 reviews
March 19, 2015
Even in the days of Mathematica, which I've used for over 10 years, I still consult this book. For one thing I know it; though I haven't memorized it, I know it well enough to quickly find what I'm looking for and in a form I readily recognize. All of its content can be extracted from Mathematica but sometimes its conventions are different and it can take time to work them out. So when I'm in a hurry I consult this reference. Also, the conventions and notations used in "Abramowitz and Stegun" (we tended not to use acronyms at that time) are still ingrained in the literature of the physical sciences, whereas, some of Mathematica's are not and a few are downright weird, to the extent I haven't figured out why they are used.
My tattered copy also is a source of fond memories of study in my youth. I can almost remember how it received each tatter. It also is nostalgic of a different time, when the capabilities of computers were much more limited than today. We had no "GUI"s then, we still "programmed"--everything! In those days the computer was more like a souped-up adding machine than the interactive device it is now. In fact I, for one, don't even think of modern computers as such. Most of what I do with mine is not computational. I tend to think of it as an environment where I perform a multitude of tasks more or less directly and not as an aid. Indeed, from that point of view (of being an aid), in those days, Abramowitz and Stegun was just as much an aid and every bit as essential as the computer.
For those thoroughly steeped in feminism it is noteworthy that this book's second editor, Irene A. Stegun was--as the name Irene once made conclusive--a woman.
In another note, I was once privileged to know the late Max Goldstein, an author cited in Abramowitz and Stegun. Max was a well-remembered presence in the 13th floor lounge of the Courant Institute, where we all met in the afternoon for coffee, tea, pastries. In those gatherings we talked about all kinds of stuff, some of which I heard for the first time there--such as neural networks, just beginning, I believe, to be recognized as an engaging problem. Max was, again to me, a warm grandfatherly person who did not disdain to talk to us students. He had been at Los Alamos during the Manhattan Project and had interesting stories to tell. (I hasten to add that Max was no "lounge lizard"; he was, in fact, very busy and integral to Courant's computing facilities.)
My tattered copy also is a source of fond memories of study in my youth. I can almost remember how it received each tatter. It also is nostalgic of a different time, when the capabilities of computers were much more limited than today. We had no "GUI"s then, we still "programmed"--everything! In those days the computer was more like a souped-up adding machine than the interactive device it is now. In fact I, for one, don't even think of modern computers as such. Most of what I do with mine is not computational. I tend to think of it as an environment where I perform a multitude of tasks more or less directly and not as an aid. Indeed, from that point of view (of being an aid), in those days, Abramowitz and Stegun was just as much an aid and every bit as essential as the computer.
For those thoroughly steeped in feminism it is noteworthy that this book's second editor, Irene A. Stegun was--as the name Irene once made conclusive--a woman.
In another note, I was once privileged to know the late Max Goldstein, an author cited in Abramowitz and Stegun. Max was a well-remembered presence in the 13th floor lounge of the Courant Institute, where we all met in the afternoon for coffee, tea, pastries. In those gatherings we talked about all kinds of stuff, some of which I heard for the first time there--such as neural networks, just beginning, I believe, to be recognized as an engaging problem. Max was, again to me, a warm grandfatherly person who did not disdain to talk to us students. He had been at Los Alamos during the Manhattan Project and had interesting stories to tell. (I hasten to add that Max was no "lounge lizard"; he was, in fact, very busy and integral to Courant's computing facilities.)
October 30, 2015
On my search of understanding the Gamma function in order to learn how to generalize factorials and then discuss with my friends how they did things back in the old days, I've met again with this beauty, a very comprehensive list of the most used functions and a quick-to-read list of everything you need to see the world in an more intimate fashion.
November 1, 2012
Comprehensive, dense and invaluable in days before Matlab, Mathematica, Wikipedia etc. The tables may be superseded by technology but still a key reference for formulae and special functions.
March 31, 2017
You may never need to know two dozen different recurrence relations for confluent hypergeometric functions. But, if that day comes, your options are A&S or its online successor http://dlmf.nist.gov/.
Displaying 1 - 4 of 4 reviews