Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class

Abstract: A limiting property of the nearest-neighbor recurrence coefficients for multiple orthogonal polynomials from a Nevai class is investigated. Namely, assuming that the nearest-neighbor coefficients have a limit along rays of the lattice, we describe it in terms of the solution of a system of partial differential equations. In the case of two orthogonality measures the differential equation becomes ordinary. For Angelesco systems, the result is illustrated numerically.