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

Courier Corporation, 1964 - Mathematics - 1046 pages

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.

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Though somewhat dated, this is the go-to book for Bessel/Hankel function tables, and tabulations of other important/magical functions like the gamma function, Euler's integral, the hypergeometric function, etc. The functions are always accompanied by a definition of the function, the roots of the function, the approximate representations, tabulated values, and more. The plots still look very funky in their coarse representations, but there are references for almost everything discussed and plotted. Is it prettier than Alpha or Mathworld? No, but the access time to get what you wanted will often be lower with a printed volume like this. Still a useful reference volume.

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http://www.math.sfu.ca/~cbm/aands/toc.htm

### Contents

 1 Mathematical Constants 2 Physical Constants and Conversion Factors 5 Elementary Transcendental Functions 65 Exponential Integral and Related Functions 227 Gamma Function and Related Functions 253 Error Function and Fresnel Integrals 295 Legendre Functions 331 Bessel Functions of Integer Order 355
 Weierstrass Elliptic and Related Functions 627 Parabolic Cylinder Functions 685 Mathieu Functions 721 Spheroidal Wave Functions 751 Orthogonal Polynomials 771 Bernoulli and Euler Polynomials Riemann Zeta Function 803 Combinatorial Analysis 821 Numerical Interpolation Differentiation and Integration 875

 Bessel Functions of Fractional Order 435 Integrals of Bessel Functions 479 Struve Functions and Related Functions 495 Confluent Hypergeometric Functions 503 Coulomb Wave Functions 537 Hypergeometric Functions 555 Jacobian Elliptic Functions and Theta Functions 567 Elliptic Integrals 587
 Probability Functions 925 Miscellaneous Functions 997 Scales of Notation 1011 Laplace Transforms 1019 Subject Index 1031 Index of Notations 1044 Copyright