By George E. Andrews
By Richard Askey
By Ranjan Roy
Publisher: Cambridge University Press
Print Publication Year:1999
Online Publication Date:May 2013
Online ISBN:9781107325937
Hardback ISBN:9780521623216
Paperback ISBN:9780521789882
Book DOI: http://dx.doi.org/10.1017/CBO9781107325937
Subjects: Algebra
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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pp. i-vi
pp. vii-xii
pp. xiii-xvi
1 - The Gamma and Beta Functions: Read PDF
pp. 1-60
2 - The Hypergeometric Functions: Read PDF
pp. 61-123
3 - Hypergeometric Transformations and Identities: Read PDF
pp. 124-186
4 - Bessel Functions and Confluent Hypergeometric Functions: Read PDF
pp. 187-239
5 - Orthogonal Polynomials: Read PDF
pp. 240-276
6 - Special Orthogonal Polynomials: Read PDF
pp. 277-354
7 - Topics in Orthogonal Polynomials: Read PDF
pp. 355-400
8 - The Selberg Integral and Its Applications: Read PDF
pp. 401-444
9 - Spherical Harmonics: Read PDF
pp. 445-480
10 - Introduction to q-Series: Read PDF
pp. 481-552
pp. 553-576
pp. 577-594
A - Infinite Products: Read PDF
pp. 595-598
B - Summability and Fractional Integration: Read PDF
pp. 599-610
C - Asymptotic Expansions: Read PDF
pp. 611-616
D - Euler–Maclaurin Summation Formula: Read PDF
pp. 617-628
E - Lagrange Inversion Formula: Read PDF
pp. 629-636
F - Series Solutions of Differential Equations: Read PDF
pp. 637-640
pp. 641-654
pp. 655-658
pp. 659-662
pp. 663-664
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