Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations (Q1902343)

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.