Multi-parametric Le Roy function

At the edge of nineteenth and twentieth century several new special functions were introduced. Among them we point out the celebrated Mittag–Leffler function which got a central role in Fractional Calculus and its applications. Less known is the so called Le Roy function used at the beginning to solve similar problems to that for Mittag–Leffler function. An interest to the Le Roy function has been revisited in the last two decades due to different questions of Analysis and Probability Theory. In our paper we introduce multi-parametric generalization of the Le Roy function and study it from the point of view of an intermediate position between the Mittag–Leffler function and another important function of Fractional Calculus, namely the Wright function.