Paper
The nearest neighbor recurrence coefficients for multiple orthogonal polynomials
Authors
Walter Van Assche
Abstract
We show that multiple orthogonal polynomials for r measures satisfy a system of linear recurrence relations only involving nearest neighbor multi-indices , where are the standard unit vectors. The recurrence coefficients are not arbitrary but satisfy a system of partial difference equations with boundary values given by the recurrence coefficients of the orthogonal polynomials with each of measures . We show how the Christoffel-Darboux formula for multiple orthogonal polynomials can be obtained easily using this information. We give explicit examples involving multiple Hermite, Charlier, Laguerre, and Jacobi polynomials.