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Monotonicity of zeros of Jacobi-Angelesco polynomials

Author: Eliel J. C. dos Santos
Journal: Proc. Amer. Math. Soc. 145 (2017), 4741-4750
MSC (2010): Primary 33C45, 26C10
Published electronically: August 1, 2017
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Abstract: We study the monotonic behaviour of the zeros of the multiple Jacobi-Angelesco orthogonal polynomials, in the diagonal case, with respect to the parameters $ \alpha ,\beta $ and $ \gamma $. We prove that the zeros are monotonic functions of $ \alpha $ and $ \gamma $ and consider some special cases of how the zeros depend on $ \beta $, especially in the presence of symmetry. As a consequence we obtain results about monotonicity of zeros of Jacobi-Laguerre and Laguerre-Hermite multiple orthogonal polynomials too.

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Additional Information

Eliel J. C. dos Santos
Affiliation: IMECC, Universidade Estadual de Campinas, Campinas-SP, 13083-859 Brazil

Keywords: Jacobi-Angelesco polynomials, zeros, monotonicity
Received by editor(s): March 11, 2016
Received by editor(s) in revised form: May 13, 2016
Published electronically: August 1, 2017
Additional Notes: The author’s research was supported by the Brazilian Science Foundation CAPES
Communicated by: Mourad E. H. Ismail
Article copyright: © Copyright 2017 American Mathematical Society

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