Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders (Paperback)

Vic Kowalenko

ISBN 10: 0521497981 / ISBN 13: 9780521497985

Published by Cambridge University Press, Cambridge, 1995

About this Item

Paperback. This work presents exciting new developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expressed in terms of hypergeometric series. Dingle's theory of terminants is then employed to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. Numerical results are used to illustrate that a complete asymptotic expansion can be made to agree with exact results for the generalised Euler-Jacobi series to any desired degree of accuracy. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable book. This work presents new developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable book. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Seller Inventory # 9780521497985

Bibliographic Details

• Title: Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 1995
• Language: English
• ISBN 10: 0521497981
• ISBN 13: 9780521497985
• Binding: Paperback
• Condition: new

About this title

Synopsis

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.

Book Description

In many real physical problems an exact solution cannot be obtained, and only approximations called asymptotic expansions exist. This work presents exciting new developments, previously neglected, in understanding the subdominant exponential terms of these expansions.