Further Geometric Behavior of the Generalized Marcum Q-Function

In this paper, we investigate a class of analytic functions associated with the generalized Marcum Q-function and its Alexander transform. We establish sufficient conditions under which these functions exhibit important geometric properties in the open unit disk, including strong starlikeness, strong convexity, and pre-starlikeness. The results presented are believed to be new and are supported by illustrative examples and consequences.