Book:George E. Andrews/Special Functions

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

More to complete later...(10+ additional chapters)


 * Bibliography
 * Index
 * Subject Index
 * Symbol Index