Special Functions
A Graduate Text

A unifying approach suitable for graduate students and mathematicians. It will serve as a textbook and as a convenient reference.

Richard Beals (Author), Roderick Wong (Author)

9780521197977, Cambridge University Press

Hardback, published 12 August 2010

466 pages, 3 b/w illus. 350 exercises
23.5 x 16 x 2.1 cm, 0.78 kg

'Although there have been many monographs on special functions since Whittaker and Watson ['s A Course of Modern Analysis, 4th edition] we can anticipate that Beals and Wong will become a classic textbook for graduate students in math, applied math, and physics. Don't delay in becoming familiar with it!' SIAM Review

The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

Preface
1. Orientation
2. Gamma, beta, zeta
3. Second order differential equations
4. Orthogonal polynomials
5. Discrete orthogonal polynomials
6. Confluent hypergeometric functions
7. Cylinder functions
8. Hypergeometric functions
9. Spherical functions
10. Asymptotics
11. Elliptic functions
References
Index.

Subject Areas: Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB]