Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders

Front Cover
Cambridge University Press, Sep 14, 1995 - Mathematics - 129 pages
0 Reviews
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

I
1
II
3
III
12
IV
20
V
24
VII
30
VIII
32
IX
44
XII
73
XIII
96
XV
100
XVI
103
XVII
105
XVIII
115
XIX
117
XX
127

XI
53

Common terms and phrases

Popular passages

Page 115 - Asymptotic expansions and analytic continuations for a class of Barnesintegrals
Page 115 - MORSE and H. FESHBACH. Methods of Theoretical Physics, Vol. I. McGraw Hill. New York, 1953.
Page 116 - AP Prudnikov, Yu.A. Brychkov and OI Marichev, Integrals and Series, Vol. 3 (Gordon & Breach, New York, 1990).