On Some Properties of q-Hahn Multiple Orthogonal Polynomials

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.

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

On Some Properties of q-Hahn Multiple Orthogonal Polynomials Articles