Jensen polynomials and the Turán and Laguerre inequalities

Abstract

In this paper we will (1) establish a relationship between the Turan inequalities and the Laguerre inequalities, (2) provide a complete characterization of functions in the Laguerre-Polya class in terms of the Turan inequalities involving the Jensen polynomials and (3) show that certain Hankel determinants of functions in the Laguerre-Polya class are nonpositive. © 1989 by Pacific Journal of Mathematics.