Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders

By N. Frankel and Vic Kowalenko

Book 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. This description may be from another edition of this product.

• Format: Electronics
• Language: English
• ISBN: 0511752512
• ISBN13: 9780511752513
• Release Date: January 1
• Publisher: Cambridge University Press