Euler type integral representations for the Kampé de Fériet functions
Tuhtasin ErgashevNational Research University «TIIAME», Tashkent, UzbekistanAnvardjan HasanovRomanovskiy Institute of Mathematics, Tashkent, Uzbekistan, Department of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, BelgiumT. K. YuldashevTashkent State University of Economics, Tashkent, Uzbekistan
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In this paper, the Kampé de Fériet functions of arbitrary order and their Euler type integral representations are studied. The general form of the integral representations for a Kampé de Fériet function are proved. Conditions, under which these representations are expressed in terms of products of two generalized hypergeometric functions, are found. The examples are identified in which the integral representation of the Kampé de Fériet function contains an elementary function or a known second order hypergeometric function in two variables.
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