Asymptotic zero distribution for a class of multiple orthogonal polynomials

Details Asymptotic zero distribution for a class of multiple orthogonal polynomials Asymptotic zero distribution for a class of multiple orthogonal polynomials

2006-06-19

arxiv.org/abs/math/0606440v1

Mathematics

Classical Analysis and ODEs

18 pages, 2 figures

Scientific paper

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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