Study of analytic function related to the Le Roy-type Mittag-Leffler function - Mehrez, K. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 517.547We study some geometric properties (such as univalence, starlikeness, convexity, and close-to-convexity) of Le Roy-type Mittag-Leffler function. In order to achieve our goal, we use new two-sided inequalities for the digamma function. Some examples are also provided to illustrate the  obtained results. Interesting consequences are deduced to show that these results improve several results available in the literature for the  two-parameter  Mittag-Leffler function.