INVERSE FACTORIAL-SERIES SOLUTIONS OF DIFFERENCE EQUATIONS

[摘要] 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

[学科分类] 数学（综合）

[关键词] asymptotic expansions;Borel transform;difference equations;exponentially improved asymptotics;factorial series;hypergeometric functions