Asymptotic zero distribution for a class of multiple orthogonal polynomials

E. Coussement, J. Coussement, W. Van Assche

Published 2006-06-19Version 1

We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these polynomials. We can apply this result to three examples of multiple orthogonal polynomials, in particular Jacobi-Pineiro, Laguerre I and the example associated with Macdonald functions. We also discuss an application to Toeplitz matrices.