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

The 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-Szegö 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.

کلیدواژه ها:

Bi-univalent function ، Gegenbauer polynomials ، Discrete probability ، Hankel and Toeplitz determinants ، Zero-truncated-Poisson series