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Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders (Paperback, New)
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Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders (Paperback, New)
Series: London Mathematical Society Lecture Note Series
Expected to ship within 18 - 22 working days
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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.
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