Journal of Approximation Theory vol:163 issue:10 pages:1427-1448
We show that multiple orthogonal polynomials for r measures satisfy a system of linear recurrence relations only involving nearest neighbor multi-indices. 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.