Electrostatic Models for Zeros of Laguerre-Sobolev Polynomials Articles uri icon

publication date

  • October 2024

start page

  • 1

end page

  • 26

issue

  • 202

volume

  • 21

International Standard Serial Number (ISSN)

  • 1660-5446

Electronic International Standard Serial Number (EISSN)

  • 1660-5454

abstract

  • Let {Sn}n0 be the sequence of orthogonal polynomials with respect to the Laguerre–Sobolev inner product

    f, gS = +∞ 0 f(x)g(x)xαe −xdx +N j=1 dj k=0 λj,kf(k)(cj)g(k)(cj),
    where λj,k  0, α > −1 and ci ∈ (−∞, 0) for i = 1, 2, . . . , N. We provide a formula that relates the Laguerre–Sobolev polynomials Sn to the classical Laguerre polynomials. We find the ladder operators for the polynomial sequence {Sn}n0 and a second-order differential equation with polynomial coefficients for {Sn}n0. We establish a sufficient condition for an electrostatic model of the zeros of orthogonal Laguerre–Sobolev polynomials. Some examples are given where this condition is either satisfied or not.

subjects

  • Mathematics

keywords

  • laguerre polynomials; sobolev orthogonality; second-order differential equation; electrostatic model