A Versatile Integral in Physics and Astronomy and Fox's H-Function

This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in physics and astronomy. Nuclear reaction rate probability integrals in nuclear physics, Kratzel integrals in applied mathematical analysis, inverse Gaussian distributions, generalized type-1, type-2, and gamma families of distributions in statistical distribution theory, Tsallis statistics and Beck-Cohen superstatistics in statistical mechanics, and Mathai's pathway model are all shown to be connected to the integral under consideration. Representations of the integral in terms of Fox's H-function are pointed out.