Algorithms for finding the structure of solutions of a system of linear partial differential equations

for an unknown function u, where PI,. . .,P, are linear partial differential operators with polynomial coefficients. Systems of differential equations for various hypergeometric functions of several variables are typical examples (see Example 1 below). The aim of this paper is to present algorithms for finding the structure of the space of solutions of such a system of differential equations. Our method consists of the following three steps:

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