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Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders by N. Frankel

Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders

by N. Frankel , Vic Kowalenko , L. Glasser
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Book cover type: Paperback
  • ISBN13: 9780521497985
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date: N/A
  • Pages: 142
  • Original Price: GBP 50.0
  • Language: English
  • Edition: N/A
  • Item Weight: 209 grams
  • BISAC Subject(s): Mathematical Analysis

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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