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arXiv · 1306.3835

Multiple orthogonal polynomials associated with an exponential cubic weight

Walter Van Assche·Galina Filipuk·Lun Zhang
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Abstract

We consider multiple orthogonal polynomials associated with the exponential cubic weight e^{-x^3} over two contours in the complex plane. We study the basic properties of these polynomials, including the Rodrigues formula and nearest-neighbor recurrence relations. It turns out that the recurrence coefficients are related to a discrete Painlev\'e equation. The asymptotics of the recurrence coefficients, the ratio of the diagonal multiple orthogonal polynomials and the (scaled) zeros of these polynomials are also investigated.

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Walter Van Assche, Galina Filipuk, Lun Zhang. 2013-06-17. Multiple orthogonal polynomials associated with an exponential cubic weight. https://doi.org/10.1016/j.jat.2014.06.006

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