SOLUTIONS TO A SYSTEM OF HYPERGEOMETRIC TYPE DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES OF THE THIRD ORDER AND ITS INTEGRAL REPRESENTATIONS

Keywords

Hypergeometric functions of several variables, system of hypergeometric equations, integral representations, linearly independent solutions.

Annotation

This article studies the properties of the Campe de Feriet function of two arguments of the third order. Integral representations and a system of partial differential equations of hypergeometric type are proved. It is indicated that the resulting system of hypergeometric type has nine linearly independent solutions at the origin.

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