Generalized distribution for bi-univalent functions defined by error and poisson distribution via bell number

Abstract

In the field of geometric function theory, generalized distributions have revealed novel insights and applications, particularly in understanding the behaviour of various complex functions. This paper focuses on estimating bounds for bi-univalent functions within probability distribution series defined by error and Poisson distributions, particularly in relation to the Bell numbers. These distributions are utilized to establish coefficient bounds, which hold significance for both the structural properties of bi-univalent functions and their applications in probability theory. By extending these methods, the study contributes to the broader framework of geometric function theory, where probability distributions offer new tools to analyze and interpret functional bounds. The findings have potential implications in areas requiring complex function estimation, including mathematical physics and statistical modeling.