Olver, F. W. J. Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations. (English) Zbl 0838.34071 Methods Appl. Anal. 1, No. 1, 1-13 (1994). A second-order linear equation is considered. It is supposed that in the neighborhood of an irregular singularity of rank one this equation has a well-known solution in the form of a special series. It is proved that asymptotically the coefficients of these series an be expanded in an asymptotic series of inverse factorials with explicit coefficients. Reviewer: V.V.Strygin (Voronezh) Cited in 3 Documents MSC: 34E05 Asymptotic expansions of solutions to ordinary differential equations 33B15 Gamma, beta and polygamma functions 34M99 Ordinary differential equations in the complex domain 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. Keywords:second-order linear equation; irregular singularity of rank one; asymptotic series PDFBibTeX XMLCite \textit{F. W. J. Olver}, Methods Appl. Anal. 1, No. 1, 1--13 (1994; Zbl 0838.34071) Full Text: DOI Digital Library of Mathematical Functions: §2.7(ii) Irregular Singularities of Rank 1 ‣ §2.7 Differential Equations ‣ Areas ‣ Chapter 2 Asymptotic Approximations §2.7(ii) Irregular Singularities of Rank 1 ‣ §2.7 Differential Equations ‣ Areas ‣ Chapter 2 Asymptotic Approximations