Jensen polynomials and the Turán and Laguerre inequalities

Thomas Curtis Craven and George Leslie Csordas

Vol. 136 (1989), No. 2, 241–260

DOI: 10.2140/pjm.1989.136.241

Abstract

In this paper we will (1) establish a relationship between the Turán inequalities and the Laguerre inequalities, (2) provide a complete characterization of functions in the Laguerre-Pólya class in terms of the Turán inequalities involving the Jensen polynomials and (3) show that certain Hankel determinants of functions in the Laguerre-Pólya class are nonpositive.

Mathematical Subject Classification 2000

Primary: 26D20

Secondary: 26C10, 33A70

Milestones

Received: 12 October 1987

Published: 1 February 1989