On Some Properties of q-Hahn Multiple Orthogonal Polynomials Articles uri icon

publication date

  • January 2010

start page

  • 1462

end page

  • 1469

issue

  • 6

volume

  • 233

international standard serial number (ISSN)

  • 0377-0427

electronic international standard serial number (EISSN)

  • 1879-1778

abstract

  • This contribution deals with multiple orthogonal polynomials of type II with respect to q-discrete measures (q-Hahn measures). In addition, we show that this family of multiple orthogonal polynomials has a lowering operator, and raising operators, as well as a Rodrigues type formula. The combination of lowering and raising operators leads to a third order q-difference equation when two orthogonality conditions are considered. An explicit expression of this q-difference equation will be given. Indeed, this q-difference equation relates polynomials with a given degree evaluated at four consecutive non-uniformed distributed points, which makes these polynomials interesting from the point of view of bispectral problems.

keywords

  • multiple orthogonal polynomials; hermite-pad´e approximation;; difference equations; q-polynomials; hahn polynomials