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Casorati type determinants of some $ \mathfrak{q}$-classical orthogonal polynomials


Authors: Antonio J. Durán and Jorge Arvesú
Journal: Proc. Amer. Math. Soc. 144 (2016), 1655-1668
MSC (2010): Primary 42C05, 33C45
DOI: https://doi.org/10.1090/proc/12839
Published electronically: September 9, 2015
MathSciNet review: 3451241
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Abstract: Some symmetries for Casorati determinants whose entries are $ \mathfrak{q}$-classical orthogonal polynomials are studied. Special attention is paid to the symmetry involving Big $ \mathfrak{q}$-Jacobi polynomials. Some limiting situations, for other related $ \mathfrak{q}$-classical orthogonal polynomial families in the $ \mathfrak{q}$-Askey scheme, namely $ \mathfrak{q}$-Meixner, $ \mathfrak{q}$-Charlier, and $ \mathfrak{q}$-Laguerre polynomials, are considered.


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Antonio J. Durán
Affiliation: Departamento de Análisis Matemático, Universidad de Sevilla, Apdo (P. O. BOX) 1160, 41080 Sevilla, Spain
Email: duran@us.es

Jorge Arvesú
Affiliation: Department of Mathematics, Universidad Carlos III de Madrid, Avda. de la Universidad, 30, 28911, Leganés, Madrid, Spain
Email: jarvesu@math.uc3m.es

DOI: https://doi.org/10.1090/proc/12839
Keywords: Orthogonal polynomials, $q$-classical polynomials, Wronskian determinant, Casorati determinant
Received by editor(s): December 4, 2014
Received by editor(s) in revised form: April 28, 2015
Published electronically: September 9, 2015
Additional Notes: This work was partially supported by MTM2012-36732-C03-03 (Ministerio de Economía y Competitividad), FQM-262, FQM-4643, FQM-7276 (Junta de Andalucía) and Feder Funds (European Union). The research of the second author was partially supported by the project MTM2012-36732-C03-01 (Ministerio de Economía y Competitividad)
Communicated by: Walter Van Assche
Article copyright: © Copyright 2015 American Mathematical Society