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.
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
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