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q-Coherent pairs and q-orthogonal polynomials

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URI: https://hdl.handle.net/10016/6046
ISSN: 0096-3003
DOI: 10.1016/S0096-3003(01)00072-8
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coherent_marcellan_amc_2002_ps.pdf (393.7 KB)
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2002-05-25
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Elsevier
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Abstract
In this paper we introduce the concept of q-coherent pair of linear functionals. We prove that if (u0,u1) is a q-coherent pair of linear functionals, then at least one of them has to be a q-classical linear functional. Moreover, we present the classification of all q-coherent pairs of positive-definite linear functionals when u0 or u1 is either the little q-Jacobi linear functional or the little q-Laguerre/Wall linear functional. Finally, by using limit processes, we recover the classification of coherent pairs of linear functionals stated by Meijer.
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26 pages, no figures.-- MSC2000 codes: 33D45, 33D15.
MR#: MR1891019 (2003d:33038)
Zbl#: Zbl 1020.33005
Keywords
q-coherence, q-Jacobi polynomials, q-Laguerre/Wall polynomials, q-orthogonal polynomials
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Applied Mathematics and Computation, 2002, vol. 128, n. 2-3, p. 191-216
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