Skellam distribution series related to categories of bi-univalent functions
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Abstract
The Skellam distribution is a probability that describes the difference between two independent random variables following a Poisson distribution. It has been widely used to model the difference in the number of events in various fields, such as sports analysis, physics, economics, and medical statistics. More recently, this distribution has received increasing attention in mathematical studies that link probability theory to complex analysis and its applications. In this research, we present a new analytic function based on the Skellam distribution. The study leads to the construction of two new spiralike categories associated with the Gregory number. We also present a new Lemma, a generalization of the lemma adopted by Zaparwa \cite{71}, which is important for studying the Fekete-Szeg\"o inequality. Using this lemma, Fekete-Szeg\"o inequalities of the new spiralike analytic categories are derived.
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References
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