Milton Abramowitz, Irene Stegun – Handbook of Mathematical Functions

Despite the growing use of computer systems, the essential want for mathematical tables continues. Tables serve an important function in preliminary surveys of issues earlier than programming for machine operation, and they’re indispensable to 1000’s of engineers and scientists with out entry to machines. Because of automated computer systems, nonetheless, and since of latest scientific advances, a higher selection of features and the next accuracy of tabulation than have been accessible till now are required.
In 1954, a convention on mathematical tables, sponsored by M.I.T. and the National Science Foundation, met to debate a modernization and extension of Jahnke and Emde’s classical tables of features. This quantity, printed 10 years later by the U.S. Department of Commerce, is the end result. Designed to incorporate a most of info and to fulfill the wants of scientists in all fields, it’s a monumental piece of work, a complete and self-contained abstract of the mathematical features that come up in bodily and engineering issues.
The e book accommodates 29 units of tables, some to as excessive as 20 locations: mathematical constants; bodily constants and conversion elements (6 tables); exponential integral and associated features (7); error perform and Fresnel integrals (12); Bessel features of integer (12) and fractional (13) order; integrals of Bessel features (2); Struve and associated features (2); confluent hypergeometric features (2); Coulomb wave features (2); hypergeometric features; Jacobian elliptic and theta features (2); elliptic integrals {9); Weierstrass elliptic and associated features; parabolic cylinder features {3); Mathieu features (2); spheroidal wave features (5); orthogonal polynomials (13); combinatorial evaluation (9); numerical interpolation, differentiation and integration (11); chance features (ll); scales of notation {6); miscellaneous features {9); Laplace transforms (2); and others.
Each of these sections is prefaced by an inventory of associated formulation and graphs: differential equations, collection expansions, particular features, and different primary relations. These represent an unusually precious reference work in themselves. The prefatory materials additionally consists of an evidence of the numerical strategies concerned in utilizing the tables that observe and a bibliography. Numerical examples illustrate the use of every desk and clarify the computation of perform values which lie outdoors its vary, whereas the editors’ introduction describes higher-order interpolation procedures. Well over100 figures illustrate the textual content.
In all, that is one of probably the most bold and helpful books of its sort ever printed, a necessary assist in all scientific and engineering analysis, drawback fixing, experimentation and discipline work. This low-cost version accommodates each web page of the unique authorities publication. Preface by A. V. Astin. Foreword by Advisory Committee, Conference on Mathematical Tables. Editors’ Introduction. Indices to Subjects, Notations.