Applications of q-Hermite Polynomials to Subclasses of Analytic and Bi-Univalent Functions

Abstract

In mathematics, physics, and engineering, orthogonal polynomials and special functions play a vital role in the development of numerical and analytical approaches. This field of study has received a lot of attention in recent decades, and it is gaining traction in current fields, including computational fluid dynamics, computational probability, data assimilation, statistics, numerical analysis, and image and signal processing. In this paper, using q-Hermite polynomials, we define a new subclass of bi-univalent functions. We then obtain a number of important results such as bonds for the initial coefficients of |a2|, |a3|, and |a4|, results related to Fekete–Szegö functional, and the upper bounds of the second Hankel determinant for our defined functions class.