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Special Functions

$80.00 (P)

Part of Encyclopedia of Mathematics and its Applications

Authors:
George E. Andrews, Pennsylvania State University
Richard Askey, University of Wisconsin, Madison
Ranjan Roy, Beloit College, Wisconsin

Date Published: January 2001
availability: Available
format: Paperback
isbn: 9780521789882

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$ 80.00 (P)
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Description

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.
- Authors are world experts in this subject
- Broad applicability throughout mathematics and physics
- Emphasis on computational formulas
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Reviews & endorsements
‘Occasionally there is published a mathematics book that one is compelled to describe as, well, let us say, special. Special Functions is certainly one of those rare books. … this treatise … should become a classic. Every student, user, and researcher in analysis will want to have it close at hand as she/he works.’ The Mathematical Intelligencer
‘… the material is written in an excellent manner … I recommend this book warmly as a rich source of information to everybody who is interested in ‘Special Functions’.’ Zentralblatt MATH
‘ … this book contains a wealth of fascinating material which is presented in a user-friendly way. If you want to extend your knowledge of special functions, this is a good place to start. Even if your interests are in number theory or combinatorics, there is something for you too … the book can be warmly recommended and should be in all good libraries.’ Adam McBride, The Mathematical Gazette
‘… it comes into the range of affordable books that you want to (and probably should have on your desk’. Jean Mawhin, Bulletin of the Belgian Mathematical Society
'The book is full of beautiful and interesting formulae, as was always the case with mathematics centred around special functions. It is written in the spirit of the old masters, with mathemtics developed in terms of formulas. There are many historical comments in the book. It can be recommended as a very useful reference.' European Mathematical Society
'… full of beautiful and interesting formulae … It can be recommended as a very useful reference.' EMS Newsletter
‘a very erudite text and reference in special functions' Allen Stenger, MAA Reviews
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Product details
- Date Published: January 2001
- format: Paperback
- isbn: 9780521789882
- length: 682 pages
- dimensions: 235 x 161 x 36 mm
- weight: 0.96kg
- availability: Available
Table of Contents
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.
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Authors
George E. Andrews, Pennsylvania State University
Richard Askey, University of Wisconsin, Madison
Ranjan Roy, Beloit College, Wisconsin