Integral representations and asymptotic behaviour of a Mittag-Leffler type function of two variables

Document Type: Original Article


LIPN, CNRS UMR 7030, Universite Paris 13, Sorbonne Paris Cite, F-93430 Villetaneuse, France.


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.