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1950 Hypergeometric functions of two variables
A. Erdélyi
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Acta Math. 83: 131-164 (1950). DOI: 10.1007/BF02392635

Abstract

The systematic investigation of contour integrals satisfying the system of partial differential equations associated with Appell's hypergeometric function F1 leads to new solutions of that system. Fundamental sets of solutions are given for the vicinity of all singular points of the system of partial differential equations. The transformation theory of the solutions reveals connections between the system under consideration and other hypergeometric systems of partial differential equations. Presently it is discovered that any hypergeometric system of partial differential equations of the second order (with two independent variables) which has only three linearly independent solutions can be transformed into the system of F1 or into a particular or limiting case of this system. There are also other hypergeometric systems (with four linearly independent solutions) the integration of which can be reduced to the integration of the system of F1.

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A. Erdélyi. "Hypergeometric functions of two variables." Acta Math. 83 131 - 164, 1950. https://doi.org/10.1007/BF02392635

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Published: 1950
First available in Project Euclid: 31 January 2017

zbMATH: 0041.39402
MathSciNet: MR37410
Digital Object Identifier: 10.1007/BF02392635

Rights: 1964 © Almqvist & Wiksells Boktryckeri

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Vol.83 • 1950
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