• SOME NEW PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTIONS OF ONE VARIABLE ASSOCIATED WITH FEYNMAN INTEGRALS

Abstract

In the present paper we study the generalized hypergeometric function  known as the I-function proposed by Rathie in 1997 which contain a certain class of Feynman Integrals, the exact partition function of the Gaussian model in statistical mechanics and several other functions as its particular cases. Convergence conditions for this function also have been derived by Rathie. During the course of study , we evaluate a new finite integral involving this function and product of two general class of polynomials. This integral is unified in nature and acts as a key formula from which we can derive as its particular cases, integrals involving a large number of simpler special functions and polynomials. For the sake of illustration, we give here some particular cases of our main integral which are also new and of interest by themselves. At the end, we give applications of our main findings by interconnecting them with the Riemann–Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electricals networks, probability theory and  statistical mechanics.