Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders
Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders
N. E. Frankel, University of Melbourne
L. Glasser, Clarkson University, New York
T. Taucher
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USDBy 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.
- Only book on this subject
- Very topical subject
Reviews & endorsements
'The book is of considerable value for the number theorist and for the analyst as well.' Monatshefte für Mathematik
Product details
September 1995Paperback
9780521497985
142 pages
229 × 152 × 8 mm
0.22kg
Available
Table of 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
- 7. Asymptotics beyond all orders
- 8. Numerics for terminant sums
- 9. Conclusion
- References
- Tables.
