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

publication date

  • April 2016

start page

  • 102

end page

  • 120

volume

  • 281

international standard serial number (ISSN)

  • 0096-3003

electronic international standard serial number (EISSN)

  • 1873-5649

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 > = 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.

keywords

  • orthogonal polynomials; freud-like weights; logarithmic potential; string equation; semi-classical linear functional