The zeros of orthogonal polynomials and Markov-Bernstein inequalities for Jacobi-exponential weights on \((-1,1)\)
Summary: Let \(U(x)=\prod_{i=1}^r |x-t_i|^{p_i}\), \(0<p<\infty\), \(-1= t_r< t_{r-1}<\cdots< t_2< t_1=1\), \(r\geq 2\), \(p_i>-1/p\), \(i=1,2,\dots,r\), and \(W= e^{-Q(x)}\) where \(Q:(-1,1)\longrightarrow [0,\infty)\). 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.
scientific article; zbMATH DE number 7290901