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Special Functions (Encyclopedia of Mathematics and its Applications) Authors: George E. Andrews, Richard Askey, Ranjan Roy Publisher: Cambridge University Press

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.

Reviewer:

This book is great. It is the best overview I have ever seen of the primary special functions, as seen from a modern viewpoint. Buy it and you will spend many happy hours reading the theorems it contains, and doing the excercizes at the end of each chapter.

Reviewer:

Though this book cannot be compared to Whittaker and Watson's classic book. It comes quite close to it. I just want to comment on the the area covers are too concentrated and the rigorous manner which is the hall mark of " Modern Analysis " is lacking. Anyway, this book deserves 5 stars.

Reviewer:

It has a very good style of writing for the nature of mathematics. It is clean, no unnecessary explanation or examples. In a way, one can feel something similar to Axler's. It is an excellent reference book. One should keep this book just as Axler's Linear Algebra Done left, Numerical Recipe, DE Knuth's Art of Programming.

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Special Functions (Encyclopedia of Mathematics and its Applications)

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