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## Abramowitz and Stegun: Handbook of Mathematical Functions

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See our disclaimer. 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 , a conference on mathematical tables, sponsored by M.

This volume, published 10 years later by the U. Department of Commerce, is the result.

## Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables | BibSonomy

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. 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 figures illustrate the text. Values on the Cut 8. Explicit Expressions 8. Recurrence Relations 8. Special Values 8. Trigonometric Expressions 8. Integral Representations 8. Summation Formulas 8. Asymptotic Expansions 8. Toroidal Functions 8. Conical Functions 8.

Relation to Elliptic Integrals 8. Integrals 8. Use and Extension of the Tables 9. Bessel Functions of Integer Order 9. Asymptotic Expansions for Large Arguments 9. Asymptotic Expansions for Large Orders 9.

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Polynomial Approximations 9. Zeros 9.

## Abramowitz and Stegun: Handbook of Mathematical Functions

Definitions and Properties 9. Asymptotic Expansions 9. Use and Extension of the Tables 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 Combinatorial Analysis Basic numbers Binomial Coefficients Multinomial Coefficients Stirling Numbers of the First Kind Stirling Numbers of the Second Kind Partitions Partitions Into Distinct Parts