Formal solutions of linear ordinary differential equations containing m-hypergeometric series

Let a linear homogeneous ordinary differential equation with polynomial coefficients over a field K be given. For a singular point of the equation, the fundamental system of formal solutions that contain a finite number of power series with coefficients belonging to the algebraic extension of K can be constructed by known algorithms. In this paper, an algorithm is suggested for construction of a space of formal solutions such that all series containing in these solutions have m-hypergeometric coefficients. The implementation of the algorithm in the computer algebra system Maple is discussed.