  In this article, we present a new two-dimensional generalization of the gamma
function based on the product of the one-dimensional generalized beta function
and the one-dimensional generalized gamma function. As will become clear later,
this generalization is also a generalization the famous formula that gives the
connection between the classical gamma and beta functions. Next we present
properties of this generalization, some series for the generalized beta
function. As a practical application of the two-dimensional generalized gamma
function, we will show how it can be used to represent a fairly wide class of
double integrals in the form of functional series.
