Zeros of orthogonal polynomials: electrostatic interpretation
Location of zeros of polynomials in the unit disc: problems and challenges
| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [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
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | Journal of Approximation Theory; v. 181, p. 18-29, MAY 2014. |
| Web of Science Citations: | 6 |
| Abstract | |
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) | |
| FAPESP's process: | 09/13832-9 - Orthogonal polynomials, special functions and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |