Abstract
Two families of Le Roy-type functions are considered in this paper, respectively with 3 and 4 indices. In the case with 4 indices, these special functions called to be as Prabhakar analogues, are proved to be entire functions and their order and type are determined. Some Mellin–Barnes-type contour integral representations as well as the Mellin transforms are derived. It is also established that the nth derivatives of the 3-parametric Le Roy-type functions are Le Roy-type functions with 4 indices (of Prabhakar type). This result is further used for representing the 3-index function in a Taylor series. Analogical relations for the integrals and derivatives of fractional orders are also obtained. Finally, some interesting particular cases of the discussed special functions are considered.
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