Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders: 214 (London Mathematical Society Lecture Note Series, Series Number 214) - Softcover

Kowalenko, Vic

Softcover

ISBN 10: 0521497981 ISBN 13: 9780521497985

Publisher: Cambridge University Press, 2013

Synopsis

This work, first published in 1995, presents 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.

About this title

Review

'The book is of considerable value for the number theorist and for the analyst as well.' Monatshefte für Mathematik

Book Description

This work presents exciting 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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2013
• Language: English
• ISBN 10: 0521497981
• ISBN 13: 9780521497985
• Binding: Paperback
• Edition number: 1
• Number of pages: 142