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2022-12-03Author
Njionou Sadjang, PatrickKalda Sawalda, D.Mboutngam, SalifouFoupouagnigni, MamaKoepf, WolframSubject
510 Mathematics Orthogonale PolynomeDifferentialgleichungRiccati-DifferentialgleichungRodrigues-FormelMetadata
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Aufsatz
On Non-linear Characterizations of Classical Orthogonal Polynomials
Abstract
Classical orthogonal polynomials are known to satisfy seven equivalent properties, namely the Pearson equation for the linear functional, the second-order differential/difference/q-differential/ 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. In this work, following previous work by Kil et al., we state and prove a non-linear characterization result for classical orthogonal polynomials on non-uniform lattices. Next, we give explicit relations for some families of these classes.
Citation
In: Mediterranean Journal of Mathematics (MedJM) Volume 20 / issue 1 (2022-12-03) eissn:1660-5454Sponsorship
Gefördert im Rahmen des Projekts DEALCitation
@article{doi:10.17170/kobra-202301197410,
author={Njionou Sadjang, Patrick and Kalda Sawalda, D. and Mboutngam, Salifou and Foupouagnigni, Mama and Koepf, Wolfram},
title={On Non-linear Characterizations of Classical Orthogonal Polynomials},
journal={Mediterranean Journal of Mathematics (MedJM)},
year={2022}
}
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2023-01-19T14:52:59Z 2023-01-19T14:52:59Z 2022-12-03 doi:10.17170/kobra-202301197410 http://hdl.handle.net/123456789/14377 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ Classical orthogonal polynomials on non-uniform lattices difference equation divided-difference equation three-term recurrence relation 510 On Non-linear Characterizations of Classical Orthogonal Polynomials Aufsatz Classical orthogonal polynomials are known to satisfy seven equivalent properties, namely the Pearson equation for the linear functional, the second-order differential/difference/q-differential/ 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. In this work, following previous work by Kil et al., we state and prove a non-linear characterization result for classical orthogonal polynomials on non-uniform lattices. Next, we give explicit relations for some families of these classes. open access Njionou Sadjang, Patrick Kalda Sawalda, D. Mboutngam, Salifou Foupouagnigni, Mama Koepf, Wolfram doi:10.1007/s00009-022-02207-y Orthogonale Polynome Differentialgleichung Riccati-Differentialgleichung Rodrigues-Formel publishedVersion eissn:1660-5454 issue 1 Mediterranean Journal of Mathematics (MedJM) Volume 20 false 10
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