The Zeros of Orthogonal Polynomials and Markov–Bernstein Inequalities for Jacobi-Exponential Weights on (−1,1)

Abstract

Let Ux=∏i=1rx−tipi, 0<p<∞, −1=tr<tr−1<⋯<t2<t1=1, r≥2, pi>−1/p, i=1,2,…,r, and W=e−Qx where Q:−1,1⟶0,∞. We give the estimates of the zeros of orthogonal polynomials for the Jacobi-Exponential weight WU on −1,1. In addition, Markov–Bernstein inequalities for the weight WU are also obtained.