On certain generalizations of hypergeometric functions of two variables
Technical University of Denmark, 1976 - Mathematics - 47 pages
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2iri 2M variables a-series a(FA a)IW analogues apply Beta integral classical results conditions for convergence denote due to Exton equation equivalent Euler's type Exton 11 FA1 a,a FD(a fU+j Function Exponents Kernel functions of 2W G-functions Gamma factors Gamma function Gauss's Horn functions hypergeometric series inequalities integral representations integrals of dimension Kernel Condition Koschmieder 18 Laplace integrals Lauricella functions Lemma m m m m m m m-1 m+1 m+1 number of variables order of summation particular Picard integral Pochhammer symbol subscripts power functions power series proofs prove r(a+a r(fa reduction formulae region of convergence relations between parameters Remark results involving Rummer's sequence subsection sufficient conditions sufficiently small summation and integration T(g+g terms of F ua"J ub"J Vandermonde's theorem vergence yv)n