The quasi-orthogonality of the derivatives of semi-classical polynomials

Medem, J. C.

doi:10.1016/s0019-3577(02)80016-7

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The Q-linear Lattices: the "Q-hahn Tableau"1

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2006

2021

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“…The last condition is usually called the admissibility condition (for a detailed study of this condition see [21,22] and references therein). That this condition was necessary was established in [23].…”

Section: The Q-linear Lattices: the "Q-hahn Tableau"mentioning

confidence: 99%

On characterizations of classical polynomials

Álvarez-Nodarse¹

2006

Journal of Computational and Applied Mathematics

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It is well known that the classical families of Jacobi, Laguerre, Hermite, and Bessel polynomials are characterized as eigenvectors of a second order linear differential operator with polynomial coefficients, Rodrigues formula, etc. In this paper we present a unified study of the classical discrete polynomials and q-polynomials of the q-Hahn tableau by using the difference calculus on linear-type lattices. We obtain in a straightforward way several characterization theorems for the classical discrete and q-polynomials of the "q-Hahn tableau". Finally, a detailed discussion of a characterization by Marcellán et al. is presented.

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Section: The Q-linear Lattices: the "Q-hahn Tableau"mentioning

confidence: 99%