  Integral representations play a prominent role in the analysis of entire
functions. The representations of generalized Mittag-Leffler type functions and
their asymptotics have been (and still are) investigated by plenty of authors
in various conditions and cases.The present paper explores the integral
representations of a special function extending to two variables the
two-parametric Mittag-Leffler type function. Integral representations of this
functions within different variation ranges of its arguments for certain values
of the parameters are thus obtained. Asymptotic expansion formulas and
asymptotic properties of this function are also established for large values of
the variables. This yields corresponding theorems providing integral
representations as well as expansion formulas.
