First-order non-homogeneous q-difference equation for Stieltjes function characterizing q-orthogonal polynomials Articles uri icon

publication date

  • May 2013

start page

  • 814

end page

  • 838

issue

  • 5

volume

  • 19

international standard serial number (ISSN)

  • 1023-6198

electronic international standard serial number (EISSN)

  • 1563-5120

abstract

  • In this paper, we give a characterization of some classical q-orthogonal polynomials in terms of a difference property of the associated Stieltjes function, i.e. this function solves a first-order non-homogeneous q-difference equation. The solutions of the aforementioned q-difference equation (given in terms of hypergeometric series) for some canonical cases, namely, q-Charlier, q-Kravchuk, q-Meixner and q-Hahn, are worked out.

keywords

  • characterization for orthogonal polynomials; moment functionals; orthogonal polynomials; q-hypergeometric series; special functions; stieltjes function