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Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations. (English) Zbl 0838.34071

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.

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.
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