Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders (London Mathematical Society Lecture Note Series)

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9780521497985: Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders (London Mathematical Society Lecture Note Series)
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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.

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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.

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

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2013. Paperback. Condition: New. New. Language: English. Brand new Book. 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. Seller Inventory # AAV9780521497985

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2013. Paperback. Condition: New. New. Language: English . Brand New Book ***** Print on Demand *****.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. Seller Inventory # AAV9780521497985

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Book Description Cambridge University Press. Paperback. Condition: New. 142 pages. Dimensions: 9.0in. x 5.9in. x 0.4in.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 Dingles 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Seller Inventory # 9780521497985

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