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

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.