On Freud-Sobolev type orthogonal polynomials Articles uri icon

publication date

  • June 2019

start page

  • 505

end page

  • 528

issue

  • 3

volume

  • 30

international standard serial number (ISSN)

  • 1012-9405

abstract

  • In this contribution we deal with sequences of monic polynomials orthogonal with respect to the Freud Sobolev-type inner product < p, q >(1) = integral(R) p(x)q(x)e(-x4) dx + M(0)p(0)q(0) + M(1)p'(0)q'(0), where p,q are polynomials, M-0 and M-1 are nonnegative real numbers. Connection formulas between these polynomials and Freud polynomials are deduced and, as an application, an algorithm to compute their zeros is presented. The location of their zeros as well as their asymptotic behavior is studied. Finally, an electrostatic interpretation of them in terms of a logarithmic interaction in the presence of an external field is given.

keywords

  • orthogonal polynomials; exponential weights; freud-sobolev type orthogonal polynomials; zeros; interlacing; electrostatic interpretation; zeros; asymptotics