期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 281, 期 -, 页码 102-120出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2016.01.048
关键词
Orthogonal polynomials; Freud-like weights; Logarithmic potential; String equation; Semi-classical linear functional
资金
- Direccion General de Investigacion Cientifica y Tecnica, Ministerio de Economia y Competitividad of Spain [MTM2012-36732-C03-01]
In this contribution we consider sequences of monic polynomials orthogonal with respect to the standard Freud-like inner product involving a quartic potential < p,q > = integral(R) p(x)q(x)e(-x4+2tx2) dx + Mp(0)q(0). We analyze some properties of these polynomials, such as the ladder operators and the holonomic equation that they satisfy and, as an application, we give an electrostatic interpretation of their zero distribution in terms of a logarithmic potential interaction under the action of an external field. It is also shown that the coefficients of their three term recurrence relation satisfy a nonlinear difference string equation. Finally, an equation of motion for their zeros in terms of their dependence on t is given. (C) 2016 Elsevier Inc. All rights reserved.
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