On Product of Hypergeometric Function, General Class of Multivariable Polynomials and a Generalized Hypergeometric Series Associated with Feynman Integrals

In this paper, we first establish a finite integral and then obtain three theorems with the help of this integral and the results given by Slater (1966). These results involve the product of hypergeometric functions, two classes of multivariable polynomials and the H -function introduce by Inayat-Hussain (1987) and further studied by Buschman an Srivastava (1990). This H -function contains certain class Feynman integrals, the exact partition function of the
Gaussian model in statistical mechanics, the polylogarithm of order p and several other functions as its particular cases. The results obtained here are quite general in nature due to the presence of two general classes of multivariable polynomials and the H -function, and we can derive from them a number of similar results involving simpler functions and polynomials. For the same of illustration, we have mentioned here three particular cases of our results which are new and of interest by themselves. References of some known results which follow from the main finding of this paper have also been given.