Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders - Paperback

by N. Frankel (Author), Vic Kowalenko (Author), L. Glasser (With)

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.