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Asymptotic zero distribution for a class of multiple orthogonal polynomials

E. Coussement·J. Coussement·W. Van Assche
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Abstract

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.

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E. Coussement, J. Coussement, W. Van Assche. 2006-06-19. Asymptotic zero distribution for a class of multiple orthogonal polynomials. https://arxiv.org/abs/math/0606440

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