NIST handbook of mathematical functions Frank W.J. Olver, editor-in-chief and mathematics editor, Daniel W. Lozier, general editor, Ronald F. Boisvert, information technology editor, Charles W. Clark, physical sciences editor ; NIST National Institute of Standards and Technology, U.S. Department of Commerce

Erscheint parallel zur freien Web-Ausgabe "NIST digital library of mathematical functions" (http://dlmf.nist.gov/) des DLMF-Projekts. - Literaturverzeichnis: Seiten 795-871

Neubearbeitung von: Handbook of mathematical functions with formulas, graphs, and mathematical tables / M. Abramowitz and I.A. Stegun, editors (1964)

Chapters: Algebraic and analytic methods -- Asymptotic approximations -- Numerical methods -- Elementary functions -- Gamma function -- Exponential, logarithmic, sine and cosine integrals -- Error functions, Dawson's and Fresnel integrals -- Incomplete gamma and related functions -- Airy and related functions -- Bessel functions -- Struve and related functions -- Parabolic cylinder functions -- Confluent hypergeometric functions -- Legendre and related functions -- Hypergeometric function -- Generalized hypergeometric functions and Meijer G-function -- q-Hypergeometric and related functions -- Orthogonal polynomials -- Elliptic integrals -- Theta functions -- Multidimensional theta functions -- Jacobian elliptic functions -- Weierstrass elliptic and modular functions -- Bernoulli and Euler polynomials -- Zeta and related functions -- Combinatorial analysis -- Functions of number theory -- Mathieu functions and Hill's equation -- Lamé functions -- Spheroidal wave functions -- Heun functions -- Painlevé transcendents -- Coulomb functions -- 3j, 6j, 9j symbols -- Functions of matrix argument -- Integrals with coalescing saddles

"The NIST Handbook has essentially the same objective as the Handbook of Mathematical Functions that was issued in 1964 by the National Bureau of Standards as Number 55 in the NBS Applied Mathematics Series (AMS). This objective is to provide a reference tool for researchers and other users in applied mathematics, the physical sciences, engineering, and elsewhere who encounter special functions in the course of their everyday work."--

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenevernatural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full colour, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Includes a DVD with a searchable PDF of each chapter.