Book:George E. Andrews/Special Functions
Jump to navigation
Jump to search
George E. Andrews, Richard Askey and Ranjan Roy: Special Functions
Published $\text {1999}$, Cambridge University Press
- ISBN 0-521-62321-9
Contents
- Preface
- CHAPTER 1: The Gamma and Beta Functions
- $\S 1$. The Gamma and Beta Integrals and Functions
- $\S 2$. The Euler Reflection Formula
- $\S 3$. The Hurwitz and Riemann Zeta Functions
- $\S 4$. Stirling's Asymptotic Formula
- $\S 5$. Gauss's Multiplication Formula for $\map \Gamma {mx}$
- $\S 6$. Integral Representation for $\map \Log {\map \Gamma x}$ and $\map \psi x$
- $\S 7$. Kummer's Fourier Expansion of $\map \Log {\map \Gamma x}$
- $\S 8$. Integrals of Dirichlet and Volumes of Ellipsoids
- $\S 9$. The Bohr-Mollerup Theorem
- $\S 10$. Gauss and Jacobi Sums
- $\S 11$. A Probabilistic Evaluation of the Beta Function
- $\S 12$. The p-adic Gamma Function
- Exercises
- CHAPTER 2: The Hypergeometric Functions
- $\S 1$. The Hypergeometric Series
- $\S 2$. Euler's Integral Representation
- $\S 3$. The Hypergeometric Equation
- $\S 4.$ The Barnes Integral for the Hypergeometric Function
- $\S 5$. Contiguous Relations
- $\S 6$. Dilogarithms
- $\S 7$. Binomial Sums
- $\S 8$. Dougall's Bilateral Sum
- $\S 9$. Fractional Integration by Parts and Hypergeometric Integrals
- Exercises
- CHAPTER 3: Hypergeometric Transformations and Identities
- $\S 1$. Quadratic Transformations
- $\S 2$. The Arithmetic-Geometric Mean and Elliptic Integrals
- $\S 3$. Transformations of Balanced Series
- $\S 4.$ Whipple's Transformation
- $\S 5$. Dougall's Formula and Hypergeometric Identities
- $\S 6$. Integral Analogs of Hypergeometric Sums
- $\S 7$. Contiguous Relations
- $\S 8$. The Wilson Polynomials
- $\S 9$. Quadratic Transformations - Riemann's View
- $\S 10$. Indefinite Hypergeometric Summation
- $\S 11$. The W-Z Method
- $\S 12$. Contiguous Relations and Summation Methods
- Exercises
More to complete later...(10+ additional chapters)
- Bibliography
- Index
- Subject Index
- Symbol Index