Hankel Determinant of Analytical Functions Closely Tied to Bell Polynomials

Applying the state-of-the-art Bell polynomials to the open unit disk, a differentialoperator θmξ, P is produced. In this paper, we shall provide a family of analytic functions related to the differential operator indicated above. The upper bound for the nonlinear functional |a2a4−a23|, otherwise known as the Hankel determinant, is our primary finding. Aside from using the Bell polynomial, the differential operator is gained using the Hadamard product. Coefficient equating and other fundamentals of classical calculus will be used in the primary finding of the upper bound.