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 low-cost
edition contains every page of the original government publication.
