Application of Gegenbauer Polynomials with Two Variables to Bi-univalency of Generalized Discrete Probability Distribution Via Zero-Truncated Poisson Distribution Series

Awolere, Tunji IbrahimOladipo, Abiodun TinuoyeAltinkaya, Sahsene2025-03-092025-03-0920242423-3900https://doi.org/10.22130/scma.2024.1987464.1235https://hdl.handle.net/20.500.12662/4631The present study is unique in exploring bi-univalent functions, which has recently garnered attention from many researchers in Geometric Function Theory (GFT). The uniqueness lies in utilizing a generalized discrete probability distribution and a zero-truncated Poisson distribution combined with generalized Gegenbauer polynomials featuring two variables. We aim to obtain coefficient bounds, the classical Fekete-Szego inequality, and Hankel and Toeplitz determinants to generalize the probability of a gambler's ruin. Additionally, using the defined bi-univalent function classes contributes to the uniqueness of the obtained results.eninfo:eu-repo/semantics/closedAccessBi-univalent functionGegenbauer polynomialsDiscrete probabilityHankel and Toeplitz determinantsZero-truncated-Poisson seriesApplication of Gegenbauer Polynomials with Two Variables to Bi-univalency of Generalized Discrete Probability Distribution Via Zero-Truncated Poisson Distribution SeriesArticle10.22130/scma.2024.1987464.12352-s2.0-851987284613Q321WOS:001272216000005N/A