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One of the key features of our viewpoint that of establishing a q-difference equation for the lefthand side of (1) can be traced back to Mellin in his study of the Gauss hypergeometric equation (see [6, [section]1.
1](a, b; c; z) corresponding to p = 2, q = 1, is the first hypergeometric function to be studied (and, in general, arises the most frequently in physical problems), and so is frequently known as "the" hypergeometric equation or, more explicitly, Gauss's hypergeometric function (Gauss 1812, Barnes 1908).
v] (z) we are dealing with in this work corresponds to the solutions of the hypergeometric equation (1.
In the present paper we obtain, in a unified way, several algebraic characteristics (recurrence and structural relations) for the solutions of the hypergeometric equation (1.
TIRAO, The matrix-valued hypergeometric equation, Proc.
1) is the usual hypergeometric equation (and Heine-Stieltjes polynomials are just hypergeometric polynomials), and for p = 2 we obtain the so-called Heun equation.