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    Joshi, N. and Lustri, C. J. 2015. Stokes phenomena in discrete Painleve I. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 471, Issue. 2177, p. 20140874.


    Weniger, Ernst Joachim 2010. Summation of divergent power series by means of factorial series. Applied Numerical Mathematics, Vol. 60, Issue. 12, p. 1429.


    Olde Daalhuis, A.B. 2009. Hyperasymptotics and hyperterminants: Exceptional cases. Journal of Computational and Applied Mathematics, Vol. 233, Issue. 2, p. 555.


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  • Proceedings of the Edinburgh Mathematical Society, Volume 47, Issue 2
  • June 2004, pp. 421-448

INVERSE FACTORIAL-SERIES SOLUTIONS OF DIFFERENCE EQUATIONS

  • A. B. Olde Daalhuis (a1)
  • DOI: http://dx.doi.org/10.1017/S0013091503000609
  • Published online: 01 July 2004
Abstract
Abstract

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

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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