INTEGRAL REPRESENTATIONS OF G-FUNCTIONS THROUGH AN INTERESTING IDEA

Some fifteen G-functions are given two integral representations and a series form each through an interesting idea of constructing statistical distributions of products and ratios of statistically independently distributed real positive scalar random variables which are equivalent to computing the Mellin convolutions of products and ratios involving two functions. These integral representations and the explicit series forms may not be available in the literature. For special values of the parameters some integral representations and series forms are available in the literature for some of the G-functions considered in this paper. But the representations given in this paper are for general parameters.