On Certain Generalizations of Hypergeometric Functions of Two Variables |
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2M variables a,b+b analogues denote ds g+s due to Exton equivalent Erdélyi Euler's type Exton 11 F(xu F₁ F₂ FA a,b FA₁ FB₂ FC₁ FD g,b;c FD₁ FD₂ Fg a,b Fg a,b;c Function Exponents Kernel functions introduced functions of 2M g'+h GA₂ Gamma factors Gamma function Gauss's GD₁ GD₂ given Horn functions hypergeometric functions hypergeometric series I(a+a I(b+b I(g+h I+J g I=i J=j inequalities integral representations integrals of dimension Koschmieder 18 Laplace integrals Lemma m m m m norm of x,y number of variables numerator parameter o-series particular Picard integral Pochhammer symbol subscripts power functions prove quadratic transformation reduction formulae region of convergence relations between parameters subsection summation and integration take f(i+j vergence хи น น