Partial Sums of the Normalized Le Roy-Type Mittag-Leffler Function

Abstract

Recently, some researchers determined lower bounds for the normalized version of some special functions to its sequence of partial sums, e.g., Struve and Dini functions, Wright functions and Miller–Ross functions. In this paper, we determine lower bounds for the normalized Le Roy-type Mittag-Leffler function Fα,βγ(z)=z+∑n=1∞Anzn+1, where An=ΓβΓα(n−1)+βγ and its sequence of partial sums (Fα,βγ(z))m(z)=z+∑n=1mAnzn+1. Several examples of the main results are also considered.