Asymptotics for recurrence coefficients of X1-Jacobi exceptional polynomials and Christoffel function

Abstract

ABSTRACTComputing asymptotics of the recurrence coefficients of -Jacobi polynomials, we investigate the limit of the 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 the corresponding theorems with respect to standard 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 Christoffel-Darboux formula also fails. It seems that these difficulties can be handled in a combinatorial way.