Nearest neighbor recurrence relations for multiple orthogonal polynomials Original Research Article

We show that multiple orthogonal polynomials for image measures image satisfy a system of linear recurrence relations only involving nearest neighbor multi-indices image, where image 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 the measures image. 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.