Exploiting q-Hermite polynomials to construct new subclass of bi-univalent functions

Orthogonal polynomials and special functions are crucial in the advancement of numerical and analytical methodologies in the fields of mathematics, physics, and engineering. In the modern era, the fields of study mentioned above have attracted considerable attention and are progressively finding their way into diverse domains, including computational probability, statistics, numerical analysis, computational fluid dynamics, data assimilation, and image and signal processing The present study introduces a novel subfamily of bi-univalent functions utilizing -Hermite polynomials. Subsequently, a multitude of significant findings are derived, including bounds for those initial coefficients of and , as well as outcomes pertaining to the Fekete-Szegö functional.