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Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach
Zusammenfassung
Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.
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@article{urn:nbn:de:hebis:34-2010083034418,
author={Foupouagnigni, Mama and Kenfack Nangho, Maurice and Mboutngam, Salifou},
title={Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach},
year={2010}
}
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2010-08-30T12:02:28Z 2010-08-30T12:02:28Z 2010 urn:nbn:de:hebis:34-2010083034418 http://hdl.handle.net/123456789/2010083034418 eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Classical orthogonal polynomials Non-uniform lattices Linear functionals Divided-difference equations Riccati equation Structure relations Functional approach 510 Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach Preprint Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function. open access Foupouagnigni, Mama Kenfack Nangho, Maurice Mboutngam, Salifou Mathematische Schriften Kassel ;; 10, 04 33C45 33D45 Mathematische Schriften Kassel 10, 04
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