A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials

Details A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials

2009-10-21

arxiv.org/abs/0910.4041v1

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1080/10236198.2010.524211

A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials satisfy. Some limiting situations when $q\to1$ are studied. Indeed, the difference equation for Hahn multiple orthogonal polynomials given in \cite{Lee} is corrected and obtained as a limiting case.

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