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Formal Solutions of Linear Ordinary Differential Equations Containing m-Hypergeometric Series

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Abstract

Let a linear homogeneous ordinary differential equation with polynomial coefficients over a field \(\mathbb{K}\) 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 \(\mathbb{K}\) 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.

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  1. Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 117967, Russia

    A. A. Ryabenko

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  1. A. A. Ryabenko
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Ryabenko, A.A. Formal Solutions of Linear Ordinary Differential Equations Containing m-Hypergeometric Series. Programming and Computer Software 28, 92–101 (2002). https://doi.org/10.1023/A:1014880918779

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