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On some properties of q-Hahn multiple orthogonal polynomials

✍ Scribed by J. Arvesú

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
551 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

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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