SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #11    ------------   OP-SF NET 6.1  ------------  January 15, 1999
From: Tom Koornwinder (
Subject: New book on Special Functions

The following is taken from the Cambridge University Press
On-line Catalog .

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.

 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
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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