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Integral representations of hypergeometric functions proved to be a veryuseful tool for studying their properties. The purpose of this paper istwofold. First, we extend the known representations to arbitrary values of theparameters and show that the extended representations can be interpreted asexamples of regularizations of integrals containing Meijer's $G$ function.Second, we give new applications of both, known and extended representations.These include: inverse factorial series expansion for the Gauss type function,new information about zeros of the Bessel and Kummer type functions, connectionwith radial positive definite functions and generalizations of Luke'sinequalities for the Kummer and Gauss type functions.

Representations of hypergeometric functions for arbitrary parameter values and their use