Special Functions

This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.

Bernoulli, Euler and Stirling Numbers. Useful Methods and Techniques. The Gamma Function. Differential Equations. Hypergeometric Functions. Orthogonal Polynomials. Confluent Hypergeometric Functions. Legendre Functions. Bessel Functions. Separating the Wave Equation. Special Statistical Distribution Functions. Elliptic Integrals and Elliptic Functions. Numerical Aspects of Special Functions. Bibliography. Notations and Symbols. Index.