Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials
We show how to obtain linear combinations of polynomials in an orthogonal sequence {Pn}n≥0, that characterize quasi-orthogonal polynomials of order k ≤ n-1. The polynomials in the sequence {Qn,k}n≥0 are obtained from Pn, by making use of parameter shifts. We use an algorithmic approach to find thes...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209521 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials / D.D. Tcheutia, A.S. Jooste, W. Koepf // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We show how to obtain linear combinations of polynomials in an orthogonal sequence {Pn}n≥0, that characterize quasi-orthogonal polynomials of order k ≤ n-1. The polynomials in the sequence {Qn,k}n≥0 are obtained from Pn, by making use of parameter shifts. We use an algorithmic approach to find these linear combinations for each family applicable, and these equations are used to prove the quasi-orthogonality of order k. We also determine the location of the extreme zeros of the quasi-orthogonal polynomials with respect to the endpoints of the interval of orthogonality of the sequence {Pn}n≥0, where possible.
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| ISSN: | 1815-0659 |