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Zbl 0838.34071
Olver, F.W.J.
Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations. (English)
[J] Methods Appl. Anal. 1, No.1, 1-13 (1994). ISSN 1073-2772

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.
[V.V.Strygin (Voronezh)]

MSC 2000:: *34E05 Asymptotic expansions (ODE)
33B15 Gamma-functions, etc.
34M99 Differential equations in the complex domain
34A25 Analytical theory of ODE

Keywords: second-order linear equation; irregular singularity of rank one; asymptotic series

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