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Jacobi–Angelesco Multiple Orthogonal Polynomials on an r-Star

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Abstract

We investigate type I multiple orthogonal polynomials on r intervals that have a common point at the origin and endpoints at the r roots of unity \(\omega ^j\), \(j=0,1,\ldots ,r-1\), with \(\omega = \exp (2\pi i/r)\). We use the weight function \(|x|^\beta (1-x^r)^\alpha \), with \(\alpha ,\beta >-1\), for the multiple orthogonality relations. We give explicit formulas for the type I multiple orthogonal polynomials, the coefficients in the recurrence relation, and the differential equation, and we obtain the asymptotic distribution of the zeros.

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Notes

  1. This is in fact Aurel Angelescu, a Romanian mathematician who wrote a Ph.D. thesis in 1916 under supervision of Paul Appell at the Sorbonne in Paris.

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Acknowledgements

This work was supported by FWO research project G.086416N and EOS project PRIMA 30889451. The authors thank the referees for their constructive suggestions.

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  1. Department of Mathematics, KU Leuven, Celestijnenlaan 200B box 2400, 3001, Leuven, Belgium

    Marjolein Leurs & Walter Van Assche

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  1. Marjolein Leurs
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  2. Walter Van Assche
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Correspondence to Walter Van Assche.

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Communicated by Percy A. Deift.

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Leurs, M., Van Assche, W. Jacobi–Angelesco Multiple Orthogonal Polynomials on an r-Star. Constr Approx 51, 353–381 (2020). https://doi.org/10.1007/s00365-019-09457-2

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