Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders

by Vic Kowalenko, N. E. Frankel, L. Glasser, T. Taucher

Overview

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.

Product Details

ISBN-13:	9780521497985
Publisher:	Cambridge University Press
Publication date:	09/14/1995
Series:	London Mathematical Society Lecture Note Series , #214
Pages:	142
Product dimensions:	5.98(w) x 9.02(h) x 0.31(d)

Table of Contents

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<p/q<7; 7. Asymptotics beyond all orders; 8. Numerics for terminant sums; 9. Conclusion; References; Tables.

Editorial Reviews

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

From the Publisher