George E. Andrews, Richard Askey, Ranjan Roy

Special Functions

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 682
• Erscheinungstermin: 3. August 2010
• Englisch
• Abmessung: 234mm x 156mm x 37mm
• Gewicht: 1018g
• ISBN-13: 9780521789882
• ISBN-10: 0521789885
• Artikelnr.: 21393797

Inhaltsangabe

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.