International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 11, Pages 745-751
Determinant inequalities for sieved ultraspherical polynomials
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.
Paul Turan first observed that the Legendre polynomials satisfy
the inequality , . 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.