Second Hankel Determinant Estimates via Gegenbauer Polynomials

Abstract

In this paper, we introduce a novel subclass of analytic functions associated with the Mittag–Leffler-type Poisson distribution connected with the Gegenbauer polynomials. We establish the Fekete–Szeg"o inequalities for functions with sharp bounds and derive coefficient bounds for the initial Taylor–Maclaurin coefficients. Moreover, we obtain upper estimates for H₂(2) for functions in the class.