Editions de l'Académie République populaire Roumaine
Revue Roumaine de Mathématiques Pures et Appliquées vol:32 issue:1 pages:15-26
Let p_n be a sequence of orthogonal polynomials on [-1,1]; let J_n(t) be a probability distribution that makes a jump of size 1/n at every zero of p_n. We investigate the asymptotic behaviour of
n(J_n(t)-J(t)), where J is the arc-sine limit of J_n. After dealing with the general case, we turn to Jacobi polynomials. Applications to quadrature formulas are included in the last section.