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On the q-Charlier Multiple Orthogonal Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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On the q-Charlier Multiple Orthogonal Polynomials
Інший ID:
2010 Mathematics Subject Classification: 42C05; 33E30; 33C47; 33C65
DOI:10.3842/SIGMA.2015.026
DOI:10.3842/SIGMA.2015.026
Посилання:
On the q-Charlier Multiple Orthogonal Polynomials / J. Arvesú, A.M. Ramírez-Aberasturis // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 20 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
The research of J. Arves´u was partially supported by the research grant MTM2012-36732-C03-01
(Ministerio de Econom´ıa y Competitividad) of Spain.
Дата:
2015
Переглядів:
567
Завантажень:
179
Анотація:
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.
