Book Details
Format
Kindle
Pages
141
Language
English
Published
Jul 11, 2013
Publisher
Cambridge University Press
ISBN-10
1107108624
ISBN-13
9781107108622
Description
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.