Olver, Frank W. J. (ed.); Lozier, Daniel W. (ed.); Boisvert, Ronald F. (ed.); Clark, Charles W. (ed.) 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. Reviewer: Hans Benker (Merseburg) Cited in 13 ReviewsCited in 2385 Documents MSC: 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions 00A20 Dictionaries and other general reference works Software:DLMF PDFBibTeX XMLCite \textit{F. W. J. Olver} (ed.) et al., NIST handbook of mathematical functions. Cambridge: Cambridge University Press (2010; Zbl 1198.00002)