A class of analytic functions related to the generalized Marcum Q-function and its geometric properties

Abstract Our aim in the present investigation is to examine certain geometric properties such as close-to-convexity, starlikeness and convexity of a certain class of analytic functions related to the generalized Marcum Q -function. Moreover, along with corollaries and examples are given. Moreover, some of these results are presented with illustrated representations. The main research tools for this paper are some bound inequalities for the lower incomplete gamma function and the monotonicity properties of the classical gamma function.