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

Copyright © 1997 Joaquin Bustoz and Mourad E. H. Ismail. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.