Matrix coefficients of the large discrete series representations of Sp(2; R) as hypergeometric series of two variables

We investigate the radial part of the matrix coefficients with minimal K-types of the large discrete series representations of Sp(2; R). They satisfy certain difference-differential equations derived from Schmid operators. This system is reduced to a holonomic system of rank 4, which is finally found to be equivalent to higher-order hypergeometric series in the sense of Appell and Kampé de Fériet.