Some Integral Properties of a General Class of Polynomials Associated with Feynman Integrals

The object of the present paper is to discuss certain integral properties of a general class of polynomials and the H-function, proposed by Inayat- Hussain which contain a certain class of Feynman integrals, the exact partition of a Gaussian model in statistical mechanics and several other functions as its particular cases. During the course of finding, we establish certain new double integral relations pertaining to a product involving a general class of polyno- mials and the H-function. These double integral relations are unified in nature and act as a key formulae from which we can obtain as their special cases, double integral relations concerning a large number of simpler special functions and polynomials. For the sake of illustration, we record here some special cases of our main results which are also new and of interest by themselves. The results established here are basic in nature and are likely to find useful applications in several fields notably electrical networks, probability theory and statistical mechanics.