Geodesic
On the $q$-Charlier Multiple Orthogonal Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015) Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce a new family of special functions, namely $q$-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to $q$-analogues of Poisson distributions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained. An explicit representation in terms of a $q$-analogue of the second of Appell's hypergeometric functions is given. A high-order linear $q$-difference equation with polynomial coefficients is deduced. Moreover, we show how to obtain the nearest neighbor recurrence relation from some difference operators involved in the Rodrigues-type formula.
Mots-clés : multiple orthogonal polynomials; Hermite–Padé approximation; difference equations; classical orthogonal polynomials of a discrete variable; Charlier polynomials; $q$-polynomials. 
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     author = {Jorge Arves\'u and Andys M. Ram{\'\i}rez-Aberasturis},
     title = {On the $q${-Charlier} {Multiple} {Orthogonal} {Polynomials}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a25/}
}
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Jorge Arvesú; Andys M. Ramírez-Aberasturis. On the $q$-Charlier Multiple Orthogonal Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a25/

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