Special Functions

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Overview

This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials. The basic building block of the functions studied in this book is the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, a number of important but relatively unknown nineteenth century results are included. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics.
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Editorial Reviews

From the Publisher
"...the authors demonstrate a superb familiarity with the historical roots of their subject...All of the chapters are beautifully written...wonderful historical insights...Special Functions will certainly emerge as the chief textbook and reference on special functions for the next several years...This book joins F. W. J. Olver's Asymptotics and Special Functions, first published in 1974 [Academic Press, New York; MR 55 #8655], as the only general books on special functions during the past three decades that belong 'in the Hobbs class,' to quote G. H. Hardy." Mathematical Reviews

"The book is packed with brief, challenging superveniences that make it a browser's delight. One of the delightful features of this book is how the sense of history, of mathematics being created and savored, informs the text. This is a splendid work, and I predict that it will be a bestseller as well." Bulletin of the American Mathematical Society

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Product Details

Table of Contents

Preface
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 Polynomials
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
A Infinite Products
B Summability and Fractional Integration
C Asymptotic Expansions
D Euler-Maclaurin Summation Formula
E LaGrange Inversion Formula
F Series Solutions of Differential Equations
Bibliography
Index
Subject Index
Symbol Index
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