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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2018 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862536405888008192 |
|---|---|
| author | Tcheutia, D.D. Jooste, A.S. Koepf, W. |
| author_facet | Tcheutia, D.D. Jooste, A.S. Koepf, W. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-03T04:30:58Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209521 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-03T04:30:58Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Tcheutia, D.D. Jooste, A.S. Koepf, W. 2025-11-24T10:31:20Z 2018 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. 1815-0659 2010 Mathematics Subject Classification: 33C05; 33C45; 33F10; 33D15; 12D10 arXiv: 1805.08954 https://nasplib.isofts.kiev.ua/handle/123456789/209521 https://doi.org/10.3842/SIGMA.2018.051 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. The authors thank the referees for the valuable comments and suggestions, which considerably improved the manuscript. This work has been supported by the Institute of Mathematics of the University of Kassel (Germany) for D.D. Tcheutia. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials Article published earlier |
| spellingShingle | Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials Tcheutia, D.D. Jooste, A.S. Koepf, W. |
| title | Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials |
| title_full | Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials |
| title_fullStr | Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials |
| title_full_unstemmed | Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials |
| title_short | Quasi-Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials |
| title_sort | quasi-orthogonality of some hypergeometric and q-hypergeometric polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209521 |
| work_keys_str_mv | AT tcheutiadd quasiorthogonalityofsomehypergeometricandqhypergeometricpolynomials AT joosteas quasiorthogonalityofsomehypergeometricandqhypergeometricpolynomials AT koepfw quasiorthogonalityofsomehypergeometricandqhypergeometricpolynomials |