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

Autor(es)

Dimitrov, Dimitar K. ^[1] ; Lun, Yen Chi ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Estadual Campinas, Inst Matemat Estat & Computacao Cient, BR-13081970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Approximation Theory; v. 181, p. 18-29, MAY 2014.
• Citações Web of Science: 6

Resumo

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. (AU)

• Processo FAPESP: 09/13832-9 - Polinômios ortogonais, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático