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.
- Unified view provides a framework that allows students a firmer grasp of the material
- Brief appendices outline material from complex analysis and Fourier analysis
- Includes succinct end-of-chapter summaries and over 350 exercises
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Reviews & endorsements
'One of the most remarkable facts of this book is its goal to be useful for self-study … highly recommended textbook.' Mathematical Reviews
'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
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Product details
- Date Published: August 2010
- format: Hardback
- isbn: 9780521197977
- length: 466 pages
- dimensions: 235 x 160 x 21 mm
- weight: 0.78kg
- contains: 3 b/w illus. 350 exercises
- availability: Available
Table of Contents
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.
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Instructors have used or reviewed this title for the following courses
- Differential Eqns
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Authors
Richard Beals, Yale University, Connecticut
Richard Beals is Professor Emeritus of Mathematics at Yale University.
Roderick Wong, City University of Hong Kong
Roderick Wong is Professor of Mathematics and Vice President for Research at the City University of Hong Kong.