SECOND HANKEL DETERMINANT FOR A CLASS OF ANALYTIC FUNCTIONS OF THE MITTAG-LEFFLER-TYPE BOREL DISTRIBUTION RELATED WITH LEGENDRE POLYNOMIALS

SECOND HANKEL DETERMINANT FOR A CLASS OF ANALYTIC FUNCTIONS OF THE MITTAG-LEFFLER-TYPE BOREL DISTRIBUTION RELATED WITH LEGENDRE POLYNOMIALS

G. Murugusundaramoorthy, S. M. El-Deeb

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Abstract

In this paper, we obtain the Fekete-Szego inequalities for the functions of complex order connected with the Mittag-Le er-type Borel distribution based upon the Legendre polynomials: Also,  nd upper bounds of the second Hankel determinant    a2a4 a23    for functions belonging to the class M  ( ;  ;  ; x).

Keywords

Fekete-Szego inequality, Second Hankel determinant, the Mittag-Le er-functions, Borel distribution, Legendre polynomials, Complex order.