Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders

Erscheinungsjahr 2013
ISBN: 978-0-521-49798-5
Verlag: Cambridge University Press

Buch, Englisch, Band 214, 141 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 217 g

Reihe: London Mathematical Society Lecture Note Series

This work presents exciting new 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.

Autoren/Hrsg.

Frankel, N.

Kowalenko, Vic

Glasser, L.

Taucher, T.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

1. Introduction; 2. Exact evaluation of Srp/q(a); 3. Properties of Sp/q(a); 4. Steepest descent; 5. Special cases of Sp/q(a) for p/q<2; 6. Integer cases for Sp/q(a) where 2