International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 1, Pages 1-7
doi:10.1155/S016117129700001X

Turán inequalities for symmetric orthogonal polynomials

Joaquin Bustoz1 and Mourad E. H. Ismail2

 1Department of Mathematics, Arizona State University, Tempe 85287, Arizona, USA
2Department of Mathematics, University of South Florida, Tampa 33620, Florida, USA
Received 22 November 1994

Abstract

A method is outlined to express a Turán determinant of solutions of a three term recurrence relation as a weighted sum of squares. This method is shown to imply the positivity of Turán determinants of symmetric Pollaczek polynomials, Lommel polynomials and q-Bessel functions.