Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders

Vic Kowalenko, N. E. Frankel, L. Glasser, T. Taucher (Autoren)

Buch | Softcover

142 Seiten

1995
Cambridge University Press (Verlag)
978-0-521-49798-5 (ISBN)

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This work presents exciting new developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable 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.

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

Erscheint lt. Verlag	14.9.1995
Reihe/Serie	London Mathematical Society Lecture Note Series
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	220 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-521-49798-1 / 0521497981
ISBN-13	978-0-521-49798-5 / 9780521497985
Zustand	Neuware