Second Hankel determinant for a class of analytic functions of the Mittag-Leffler-type Borel distribution related with legendre polynomials

Abstract

In this paper, we obtain the Fekete-Szegö inequalities for the functions of complex order connected with the Mittag-Leffler-type Borel distribution based upon the Legendre polynomials. Also, find upper bounds of the second Hankel determinant ¬|a?a? ? a²?| for functions belonging to the class M?? (?, ?, ?, x).