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Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders (London Mathematical Society Lecture Note Series, Series Number 214)
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ISBN: 0521497981
Author: Kowalenko, Vic
Condition: New
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.
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Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders (London Mathematical Society Lecture Note Series, Series Number 214)