Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables

By Irene Stegun and Milton Abramowitz

Book Overview

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 over100 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 contains every page of the original government publication.

• Format: Paperback
• Language: English
• ISBN: 0486612724
• ISBN13: 9780486612720
• Release Date: June 1965
• Publisher: Dover Publications
• Length: 1072 Pages
• Weight: 3.49 lbs.
• Dimensions: 1.6" x 8.0" x 10.5"

Customer Reviews

A seminal work

The amount of material in this book still stuns me, as well as the care that was taken in compiling it. Its influence is still felt in that many people still use its nomenclature for special functions. Many of the comments of the other reviewers are valid. However, one should realize this book came from another era, one in which the availability of digital computation resources weren't so prevalent or cheap as they are today. When one had to evaluate an expression to more significant figures than available on a slide rule, the calculation had to be done with logarithms and tables. It was noxious drudgery and error-prone to boot. This book covers many, if not most, of the special functions a technical person will be likely to encounter during his or her career. The level of presentation is approximately at what one could expect of a four year technical degree that has had exposure to the normal year and a half of elementary calculus, a semester or two of advanced calculus including differential equations, a semester of complex variables, and possibly a numerical analysis course. However, the book can still be used profitably even if you haven't had all that background. For $25 new or $5-10 used, it's hard to get this kind of information density for such low cost. My copy is pretty beat up; it's marked at $6.95 and I probably bought it in the late 1960's or early 1970's. The NIST is working on a digital replacement of Abramowitz and Stegun. Visit their website for an update.

Improved my insight and understanding each time used

I have enjoyed using this book over quite some time. Its comprehensiveness promised to never let me down. It did keep the promise since the late seventies. Whenever I needed a clearer picture, perhaps a reason why a function did behave the way it did, I found the additional clarification here. Glad it exists.

The most important handbook I ever seen

This book is a compendious of mathematical tables, formulas and graphics. It contains a very complete table of analytical integrals, differential equations and numerical series. Furthermore there are tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration and techniques for point interpolation and function approximation. There is a whole section for mathematical and physical constants as fractions and powers of Pi, e and prime numbers. Statistics are also discussed by presenting combinatorial analysis and probability functions. In its more than 1000 pages, almost all mathematical areas are treated. Every time you need same mathematical relation or information you will find it on this book. If you work with mathematical research or numerical computing you must have this book.

A good overall summary of orthogonal functions.

This book is a good overall summary of orthogonal functions. I did find it to be somewhat incomplete for prolate spheroidal wave functions, having to refer to the book from which they took their information. Overall, this book is a must-have for any physicist or mathematician. You can't beat the information per dollar density.

A & S is one of the true "MUST HAVES"

A & S's Handbook of Mathematical Functions is an absolute must have for any lover of mathematics. The explanations are top rate. With the abilities of computers to tabulate numbers rapidly, the value of the tables is questionable. But the mathematical coverage is absolutely without equal. Any function you can think of, and some that you probably can't are covered in steamy, lurid detail. The paperback is such a great value that it makes me whinge to imagine that any lover of mathematics could possibly pass it by.