Harmonic functions associated with Pascal distribution series

Abstract

The primary objective of this paper is to explore the application of a specific convolution operator, which incorporates the Pascal distribution series. Through this investigation, we establish essential inclusion relations between the harmonic class HΥ(ϱ,ξ) and other classes of harmonic functions, namely, harmonic starlike functions and harmonic convex functions, all defined within the confines of the open unit disk. Moreover, we derive consequential outcomes from our main findings. The study delves into the intriguing interplay among these harmonic function classes, shedding light on their underlying properties and mutual connections. The presented results contribute to a deeper understanding of harmonic functions and provide a valuable basis for further research in this area.