Asymptotics for Recurrence Coefficients of X1-Jacobi Polynomials and Christoffel Function

Abstract

Computing asymptotics of the recurrence coefficients of X1-Jacobi polynomials we investigate the limit of Christoffel function. We also study the relation between the normalized counting measure based on the zeros of the modified average characteristic polynomial and the Christoffel function in limit. The proofs of corresponding theorems with respect to ordinary orthogonal polynomials are based on the three-term recurrence relation. The main point is that exceptional orthogonal polynomials possess at least five-term formulae and so the Christoffel-Darboux formula also fails. It seems that these difficulties can be handled in combinatorial way.