Abstract:
In the present paper, the author has introduced a new special function namely -function of two variables in the literature of special functions. The definition, convergence, asymptotic behaviors have been considered. Next, we obtain some properties of -function of two variables. Later on, the author establish a series representation for the -function of two variables. Some interesting special cases of -function of two variables by comparing the series representation of -function of two variables and -function of one variable is also established. In the last, the author has given two special cases of -function of two variables which are not the special cases of -function of two variables.

Keywords: function, -function of two variables, -function, Series representation. (2000 Mathematics Subject Classification: 33C70)