Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders
Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders
Vic Kowalenko, University of Melbourne
N. E. Frankel, University of Melbourne
L. Glasser, Clarkson University, New York
T. Taucher
N. E. Frankel, University of Melbourne
L. Glasser, Clarkson University, New York
T. Taucher
September 1995
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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.
- 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.
