Applications of -Borel distribution series involving -Gegenbauer polynomials to subclasses of bi-univalent functions.

This study introduces a new class of bi-univalent functions in the open disk using -Borel distribution series and -Gegenbauer polynomials. It provides estimates for the Taylor coefficients and for this family of functions, as well as solutions for the Fekete-Szegö functional problems associated with this subclass. The study presents various innovative findings that result from the unique parameters used in the main results.

The Miller-Ross Poisson distribution and its applications to certain classes of bi-univalent functions related to Horadam polynomials.

Within the scope of this research, we introduce a novel category of bi-univalent functions. Horadam polynomials are utilized to characterize these functions by utilizing series from the Poisson distribution of the Miller-Ross type. Functions from these new categories have been used to construct estimates for the Fekete-Szego functional, as well as estimates of the Taylor-Maclaurin coefficients and .