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arXiv · 1003.4692

Asymptotic zero distribution of multiple orthogonal polynomials associated with Macdonald functions

Lun Zhang·Pablo Román
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Abstract

We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). Based on the four-term recurrence relation, it is shown that, after proper scaling, the sequence of normalized zero counting measures converges weakly to the first component of a vector of two measures which satisfies a vector equilibrium problem with two external fields. We also give the explicit formula for the equilibrium vector in terms of solutions of an algebraic equation.

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Lun Zhang, Pablo Román. 2011-02-02. Asymptotic zero distribution of multiple orthogonal polynomials associated with Macdonald functions. https://arxiv.org/abs/1003.4692

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