An electrostatic model for zeros of perturbed Laguerre polynomials Articles uri icon

publication date

  • May 2014

start page

  • 1733

end page

  • 1747

issue

  • 5

volume

  • 142

international standard serial number (ISSN)

  • 0002-9939

electronic international standard serial number (EISSN)

  • 1088-6826

abstract

  • In this paper we consider the sequences of polynomials {Q(alfa) n}n≥0, orthogonal with respect to the inner product where dmu(x) = xalfae-x is the Laguerre measure on R+, alfa>-1, cj < 0, aj > 0 and f, g are polynomials with real coefficients. We first focus our attention on the representation of these polynomials in terms of the standard Laguerre polynomials. Next we find the explicit formula for their outer relative asymptotics, as well as the holonomic equation that such polynomials satisfy. Finally, an electrostatic interpretation of their zeros in terms of a logarithmic potential is presented. © 2014 American Mathematical Society.

keywords

  • electrostatic interpretation; orthogonal polynomials