UTILIZING THE POISSON PROBABILITY DISTRIBUTION SERIES FOR A SPECIFIC CLASS OF ANALYTIC FUNCTIONS THROUGH THE SALGEAN DERIVATIVE OPERATOR AND STIRLING NUMBERS

Abstract

In this investigation, we will utilize the Salagean derivative operator in conjunction with Stirling numbers to analyze the class (Ω(s),θ) of analytic functions characterized by negative coefficients. We will establish both necessary and sufficient conditions, as well as inclusion relations, for series corresponding to the Poisson distribution. Furthermore, we will introduce an integral operator related to the Poisson distribution series, demonstrating its membership within this framework. A practical example will be provided to illustrate and underscore the connection between geometric function theory and statistics.