NIST handbook of mathematical functions. (English) Zbl 1198.00002

Cambridge: Cambridge University Press (ISBN 978-0-521-19225-5/hbk; 978-0-521-14063-8/pbk). xv, 951 p., with cd-rom. (2010).
The NIST Handbook of Mathematical Functions, together with its Web counterpart, the NIST Digital Library of Mathematical Functions (DLMF) http://dlmf.nist.gov/, is the culmination of a project that was conceived in 1996 at the National Institute of Standards and Technology (NIST). The Handbook had two equally important goals:
To develop an authoritative replacement for the Handbook of Mathematical Functions, published in 1964 by the National Bureau of Standards; and to disseminate essentially the same information from a public Web site operated by NIST [http://dlmf.nist.gov/].
The Handbook has the following contents:
1 Algebraic and Analytic Methods;
2 Asymptotic Approximations;
3 Numerical Methods;
4 Elementary Functions;
5 Gamma Function;
6 Exponential, Logarithmic, Sine, and Cosine Integrals;
7 Error Functions, Dawson’s and Fresnel Integrals;
8 Incomplete Gamma and Related Functions;
9 Airy and Related Functions;
10 Bessel Functions;
11 Struve and Related Functions;
12 Parabolic Cylinder Functions;
13 Confluent Hypergeometric Functions;
14 Legendre and Related Functions;
15 Hypergeometric Function;
16 Generalized Hypergeometric Functions and Meijer G-Function;
17 \(q\)-Hypergeometric and Related Functions;
18 Orthogonal Polynomials;
19 Elliptic Integrals;
20 Theta Functions;
21 Multidimensional Theta Functions;
22 Jacobian Elliptic Functions;
23 Weierstrass Elliptic and Modular Function;
24 Bernoulli and Euler Polynomials;
25 Zeta and Related Functions;
26 Combinatorial Analysis;
27 Functions of Number Theory;
28 Mathieu Functions and Hill’s Equation;
29 Lamé Functions;
30 Spheroidal Wave Functions;
31 Heun Functions;
32 Painlevé Transcendents;
33 Coulomb Functions;
34 \(3j\), \(6j\), \(9j\) Symbols;
35 Functions of Matrix Argument;
36 Integrals with Coalescing Saddles.


33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions
00A20 Dictionaries and other general reference works