最 低 价：￥43.10
定 价：￥88.00
作 者：安德鲁斯（Andrews,G.），阿斯基（Askey,R.），罗伊（Roy,R.） 著 著
出 版 社：清华大学出版社
出版时间：2004-8-1
I S B N：9787302090892
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| Preface 1 The Gamma and Beta Functions 1.1 The Gamma and Beta Integrals and Functions 1.2 The Euler Reflection Formula 1.3 The Hurwitz and Riemann Zeta Functions 1.4 Stirling's Asymptotic Formula 1.5 Gauss's Multiplication Formula for 1.6 Integral Representations for Log 1.7 Kummer's Fourier Expansion of Log 1.8 Integrals of Dirichlet and Volumes of Ellipsoids 1.9 The Bohr-Mollerup Theorem 1.10 Gauss and Jacobi Sums 1.11 A Probabilistic Evaluation of the Beta Function 1.12 The p-adic Gamma Function Exercises 2 The Hypergeometric Functions 2.1 The Hypergeometric Series 2.2 Euler's Integral Representation 2.3 The Hypergeometric Equation 2.4 The Barnes Integral for the Hypergeometric Function 2.5 Contiguous Relations 2.6 Dilogarithms 2.7 Binomial Sums 2.8 Dougall's Bilateral Sum 2.9 Fractiona Integration by Parts and Hypergeometric Integrals Exercises 3 Hypergeometric Trans formations and Identities 3.1 Auadratic Transformations 3.2 The Arithmetic-Geometric Mean and Elliptic Integrals 3.3 Trasformations of Balanced Series 3.4 Whipple's Formula and Hypergeometric Identities 3.5 Integral Analogs of Hypergeometric Sums 3.6 Contiguous Relations 3.7 Quadratic Transformations-Riemann's View 3.8 Indefinite Hypergeometric Summation 3.9 The W-ZMetod 3.10 Contiguous Relations and Summation Methods Exercises 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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