Publication: On some properties of q-Hahn multiple orthogonal polynomials
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2010-01-15
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Elsevier
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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.
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8 pages, no figures.-- MSC2000 code: *33-99.-- Issue title: "Special Functions, Information Theory, and Mathematical Physics" (dedicated to Professor Jesus Sánchez Dehesa on the occasion of his 60th birthday).
Zbl#: Zbl pre05650063
Zbl#: Zbl pre05650063
Keywords
Multiple orthogonal polynomials, Hermite-Padé approximation, Difference equations, q-polynomials, Hahn polynomials
Bibliographic citation
Journal of Computational and Applied Mathematics, 2010, vol. 233, n. 6, p. 1462-1469