On the q-Charlier Multiple Orthogonal Polynomials

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 28 Mar 2015Embargo end date: 01 Jan 2014Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659,

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Authors: Arves??, J.; Ram??rez-Aberasturis, A.M.;

doi: 10.3842/sigma.2015.026 , 10.48550/arxiv.1411.2000

arXiv: 1411.2000

handle: 10016/23312

On the q-Charlier Multiple Orthogonal Polynomials

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Abstract

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.

Related Organizations

Carlos III University Madrid (UC3M)
Spain
Complutense University of Madrid
Spain
Carlos III University of Madrid
Spain

Keywords

Difference equations, Charlier polynomials, Matemáticas, Multiple orthogonal polynomials, Hermite-Padé approximation, Other special orthogonal polynomials and functions, difference equations, multiple orthogonal polynomials, q-Polynomials, Appell, Horn and Lauricella functions, Mathematics - Classical Analysis and ODEs, Classical orthogonal polynomials of a discrete variable, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Other functions coming from differential, difference and integral equations, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, classical orthogonal polynomials of a discrete variable, $q$-polynomials

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