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INVERSE FACTORIAL-SERIES SOLUTIONS OF DIFFERENCE EQUATIONS

Published online by Cambridge University Press:  01 July 2004

A. B. Olde Daalhuis
A. B. Olde Daalhuis
Affiliation:
School of Mathematics, King’s Buildings, University of Edinburgh, Edinburgh EH9 3JZ, UK (adri@maths.ed.ac.uk)
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Abstract

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We obtain inverse factorial-series solutions of second-order linear difference equations with a singularity of rank one at infinity. It is shown that the Borel plane of these series is relatively simple, and that in certain cases the asymptotic expansions incorporate simple resurgence properties. Two examples are included. The second example is the large $a$ asymptotics of the hypergeometric function ${}_2F_1(a,b;c;x)$.

AMS 2000 Mathematics subject classification: Primary 34E05; 39A11. Secondary 33C05

Keywords

asymptotic expansionsBorel transformdifference equationsexponentially improved asymptoticsfactorial serieshypergeometric functions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 2 , June 2004 , pp. 421 - 448
Copyright
Copyright © Edinburgh Mathematical Society 2004