Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders

ISBN-13: 9780521497985 / Angielski / Miękka / 1995 / 142 str.

N. Frankel; L. Glasser; T. Taucher

Opis

By considering special exponential series arising in number theory, the authors derive the generalized Euler-Jacobi series, expressed in terms of hypergeometric series. They then employ Dingle's theory of terminants to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. The authors use numerical results to show that a complete asymptotic expansion can be made to agree with exact results for the generalized Euler-Jacobi series to any desired degree of accuracy.

Recenzje

'The book is of considerable value for the number theorist and for the analyst as well.' Monatshefte für Mathematik

Spis treści

1. Introduction; 2. Exact evaluation of Srp/q(a); 3. Properties of Sp/q(a); 4. Steepest descent; 5. Special cases of Sp/q(a) for p/q<2; 6. Integer cases for Sp/q(a) where 2