Subfamilies of Bi-Univalent Functions Associated with the Imaginary Error Function and Subordinate to Jacobi Polynomials

Numerous researchers have extensively studied various subfamilies of the bi-univalent function family utilizing special functions. In this paper, we introduce and investigate a new subfamily of bi-univalent functions, which is defined on the symmetric domain. This subfamily is connected to the Jacobi polynomial through the imaginary error function. We derive the initial coefficients of the Maclaurin series for functions in this subfamily, and analyze the Fekete–Szegő inequality for these functions. Additionally, by specializing the parameters in our main results, we deduce several new and significant findings.