International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 11, Pages 745-751
doi:10.1155/S0161171201004896

Determinant inequalities for sieved ultraspherical polynomials

J. Bustoz1 and I. S. Pyung2

1Department of Mathematics, Arizona State University, Tempe 85287, AZ, USA
2Korean Naval Academy, Kyung-Nam, Chin-Hae 645-797, Korea

Received 28 March 2000

Copyright © 2001 J. Bustoz and I. S. Pyung. 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

Paul Turan first observed that the Legendre polynomials satisfy the inequality Pn2(x)−Pn−1(x)Pn(x)>0, −1<x<1. Inequalities of this type have since been proved for both classical and nonclassical orthogonal polynomials. In this paper, we prove such an inequality for sieved orthogonal polynomials of the second kind.