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.

Contenu

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