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Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials

Journal article published in 2014 by Dimitar K. Dimitrov ORCID, Yen Chi Lun, Yen Chi Lun
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) ; Processo FAPESP: 09/13832-9 ; Denote by (P) over cap ((alpha,beta))(n) (x) the X-1-Jacobi polynomial of degree n. These polynomials were introduced and studied recently by Gomez-Ullate, Kamran and Milson in a series of papers. In this note we establish some properties of the zeros of (P) over cap ((alpha,beta))(n) (x), such as interlacing and monotonicity with respect to the parameters a and beta. They turn out to possess an electrostatic interpretation. The vector, whose components are the zeros, is a saddle point of the energy of the corresponding logarithmic field. (c) 2014 Elsevier Inc. All rights reserved.