# Hypergeometric Functions of $2 \times 2$ Matrix Argument are Expressible in Terms of Appell's Functions $F_4$

Tom Koornwinder and Ida Sprinkhuizen-Kuyper
Proceedings of the American Mathematical Society
Vol. 70, No. 1 (Jun., 1978), pp. 39-42
DOI: 10.2307/2042581
Stable URL: http://www.jstor.org/stable/2042581
Page Count: 4

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It is proved that the hypergeometric function of $2 \times 2$ matrix argument is expressible as a solution of the partial differential equations for Appell's function $F_4$. As a result the first-mentioned function can be written as a sum of two $F_4$-functions.