(untitled) (European Journal of Pure and Applied Mathematics, 2025)
A unique family of bi-univalent functions, commonly known as functions that are defined on the symmetric domain, is presented and investigated in this paper. We also presented and examined the subfamily of the functions. The imaginary error function establishes a connection between the relevant subfamily and the Jacobi polynomial. In addition to this, we obtained the initial coefficients of the Maclaurin series for functions that are members of this subfamily. Additionally, we proceed to do an analysis of the Fekete-Szegö inequality associated with these functions.