On polynomials associated with an Uvarov modification of a quartic potential Freud-like weight

Alejandro Arceo, Edmundo J. Huertas and Francisco Marcellán

Applied Mathematics and Computation, 2016, vol. 281, issue C, 102-120

Abstract: 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〉=∫Rp(x)q(x)e−x4+2tx2dx+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.

Keywords: Orthogonal polynomials; Freud-like weights; Logarithmic potential; String equation; Semi-classical linear functional (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300316300480
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:281:y:2016:i:c:p:102-120

DOI: 10.1016/j.amc.2016.01.048

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().