## Multiple hypergeometric functions and applications |

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analytical continuation Appell functions application asymptotic Bessel function Beta Distribution Cartesian equation Chapter characteristic function confluent form confluent hypergeometric function contour of integration deduced defined denote density function Dirichlet Distribution discussed employed encircling Euler integral example expansions Exton.H Feriet function function F Gamma Distribution gamma functions Gauss function given Horn functions Humbert functions hyper hypergeometric series integral formula integral representations integrand integrate term involving Kampe de Feriet Laplace integrals Laplace type Lauricella functions less than unity m+n+p moduli multiple hypergeometric functions multiple integral multiple series multiplication theorems obtained parameters partial differential system polynomials Re(a Re(b readily region of convergence relations respectively right hand member Saran Section series representation similar singular manifolds singular point solutions Srivastava Srivastava.H. M. summation term by term theorem theory transformations triple hypergeometric functions valid variable of integration written zero