Preliminary text. Do not use. This book is about the many properties of hypergeometric functions - their number theoretic, function theoretic, combinatorial and applied mathematics appearances. Hypergeometric functions, the most important non-elementary functions, hold great arithmetic and geometric importance, while being the basic blocks of quantum mechanical and engineering and physical computations.

Inhalt

• Preface * Introduction by R. Askey * Hypergeometric and generalized hypergeometric functions in one and many variables * Classical hypergeometric function identities - functional theoretic and combinatorial interpretation. q-basic series * Evaluation of hypergeometric functions at special values - \Gamma - factors and period relations * Reducible cases of hypergeometric equations * Applications of the Lagrange inversion formula * Padé approximations to hypergeometric functions as hypergeometric polynomials * Special hypergeometric functions - polylogarithms and other functions * Diophantine approximations and measures of irrationality * Hypergeometric function evaluation and calculation - physics and applied mathematics * Appendix by W. Gosper. Hypergeometric identities * References