On some properties of q-Hahn multiple orthogonal polynomials

Authors:
J. Arvesú
Affiliations:
Department of Mathematics, Universidad Carlos III de Madrid, Avda. de la Universidad, 30, 28911, Leganés, Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 5
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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.