International Journal of Mathematics and Mathematical Sciences (Jan 2001)
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.