This volume presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series.

Special Functions ICM Edition (Encyclopedia of Mathematics and its Applications, Series Number 71)

Science & Math

Andrews, George E.

Askey, Richard

Roy, Ranjan

Mathematics

Cambridge University Press

Special Functions (Encyclopedia of Mathematics and its Applications, Series Number 71)

<p>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.</p>

Reference

Encyclopedias & Subject Guides

<p>Originally presented as lectures, the theme of this volume is that one studies orthogonal polynomials and special functions not for their own sake, but to be able to use them to solve problems. The author presents problems suggested by the isometric embedding of projective spaces in other projective spaces, by the desire to construct large classes of univalent functions, by applications to quadrature problems, and theorems on the location of zeros of trigonometric polynomials. There are also applications to combinatorial problems, statistics, and physical problems.</p>

Orthogonal Polynomials and Special Functions (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 21)

Society for Industrial and Applied Mathematics

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