Exploring the Inclusion Properties of Integral Operators Related to the Pascal Distribution Series in Certain Subclasses of Univalent Functions

This study investigates the geometric characteristics of integral operators connected with the Pascal distribution series. The objective of this article is to establish conditions on the parameters of these operators by utilizing coefficient bounds from class $\mathcal{R}_{\wp,\upsilon}^{\tau}(\gamma)$. Also, the study analyzes the inclusion outcomes of integral operators related to the Pascal distribution series within various subclasses of analytic functions. The findings presented here incorporated previously published results as specific instances.