Topic #11 ------------ OP-SF NET 6.1 ------------ January 15, 1999 ~~~~~~~~~~~~~ From: Tom Koornwinder (thk@wins.uva.nl) Subject: New book on Special Functions The following is taken from the Cambridge University Press On-line Catalog (http://www.cup.org/Titles/62/0521623219.html). Special Functions Andrews, George E., Askey, Richard and Roy, Ranjan Special functions, which include the trigonometric functions, have been used for centuries. Their role in the solution of differential equations was exploited by Newton and Leibniz, and the subject of special functions has been in continuous development ever since. In just the past thirty years several new special functions and applications have been discovered. This treatise presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series. It includes both important historical results and recent developments and shows how these arise from several areas of mathematics and mathematical physics. Particular emphasis is placed on formulas that can be used in computation. The book begins with a thorough treatment of the gamma and beta functions that are essential to understanding hypergeometric functions. Later chapters discuss Bessel functions, orthogonal polynomials and transformations, the Selberg integral and its applications, spherical harmonics, q-series, partitions, and Bailey chains. This clear, authoritative work will be a lasting reference for students and researchers in number theory, algebra, combinatorics, differential equations, applied mathematics, mathematical computing, and mathematical physics. Contents: 1. The Gamma and Beta Functions 2. The Hypergeometric Functions 3. Hypergeometric Transformations and Identities 4. Bessel Functions and Confluent Hypergeometric Functions 5. Orthogonal Polynomials 6. Special Orthogonal Transformations 7. Topics in Orthogonal Polynomials 8. The Selberg Integral and its Applications 9. Spherical Harmonics 10. Introduction to q-Series 11. Partitions 12. Bailey Chains Appendix 1 Infinite Products Appendix 2 Summability and Fractional Integration Appendix 3 Asymptotic Expansions Appendix 4 Euler-Maclaurin Summation Formula Appendix 5 Lagrange Inversion Formula Appendix 6 Series Solutions of Differential Equations Encyclopedia of Mathematics and its Applications 71 Subject: mathematics 1998 6 1/8 x 9 1/4 c. 560 pp. Hardback 0-521-62321-9 $85.00 George Andrews' Book "Partitions" has been reprinted in a paperback edition by Cambridge University Press with the correction of some misprints. Here is the information (from http://www.cup.org/Titles/63/052163766X.html): Cambridge Mathematical Library Subject: mathematics 1998 6 1/8 x 9 3/4 269 pp. 12 line diagrams 5 tables Paperback 0-521-63766-X $29.95

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