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Proceedings of the American Mathematical Society

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Hypergeometric functions of $ 2\times 2$ matrix argument are expressible in terms of Appel's functions $ F\sb{4}$


Authors: Tom Koornwinder and Ida Sprinkhuizen-Kuyper
Journal: Proc. Amer. Math. Soc. 70 (1978), 39-42
MSC: Primary 33A30
DOI: https://doi.org/10.1090/S0002-9939-1978-0473251-6
MathSciNet review: 0473251
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Abstract: 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.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0473251-6
Keywords: Hypergeometric functions of matrix argument, Appell's hypergeometric functions $ {F_4}$
Article copyright: © Copyright 1978 American Mathematical Society