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  3. Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders
  • Cited by 10
Publisher:
Cambridge University Press
Online publication date:
August 2013
Print publication year:
1995
Online ISBN:
9780511752513
DOI:
https://doi.org/10.1017/CBO9780511752513
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Real and Complex Analysis
Series:
London Mathematical Society Lecture Note Series (214)
Information

Book description

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.

Reviews

‘The book is of considerable value for the number theorist and for the analyst as well.’

Source: Monatshefte für Mathematik

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