Otro
Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials
Registro en:
Journal Of Approximation Theory. San Diego: Academic Press Inc Elsevier Science, v. 181, p. 18-29, 2014.
0021-9045
10.1016/j.jat.2014.01.007
WOS:000335277200004
Autor
Dimitrov, Dimitar K.
Lun, Yen Chi
Resumen
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. Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)