Certain integral properties pertaining to special functions

The aim of the present paper is to study certain integral properties of M-series [7], a general class of polynomials [9], Fox’s H-function [3] and H̄function [6] which contains a certain class of Feynman integrals, exact partition of a Gaussian model in statistical mechanics and several other functions as its particular cases. The main results of our paper are unified in nature and capable of yielding a very large number of corresponding interesting results (new and known) involving simpler special functions and polynomials as special cases of our formulae. The results established here are basic in nature and are likely to find useful application in several fields notably electrical networks, probability theory and statistical mechanics etc.