Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases
We introduce the notion of ''hypergeometric'' polynomials with respect to Newtonian bases. We find the necessary and sufficient conditions for the polynomials Pn(x) to be orthogonal. For the special cases where the sets λn correspond to the classical grids, we find the complete s...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147742 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735289252839424 |
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| author | Vinet, L. Zhedanov, A. |
| author_facet | Vinet, L. Zhedanov, A. |
| citation_txt | Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We introduce the notion of ''hypergeometric'' polynomials with respect to Newtonian bases. We find the necessary and sufficient conditions for the polynomials Pn(x) to be orthogonal. For the special cases where the sets λn correspond to the classical grids, we find the complete solution to these conditions and observe that it leads to the most general Askey-Wilson polynomials and their special and degenerate classes.
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| first_indexed | 2025-12-07T19:47:17Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147742 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:47:17Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vinet, L. Zhedanov, A. 2019-02-15T19:01:01Z 2019-02-15T19:01:01Z 2016 Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C05; 42C15 DOI:10.3842/SIGMA.2016.048 https://nasplib.isofts.kiev.ua/handle/123456789/147742 We introduce the notion of ''hypergeometric'' polynomials with respect to Newtonian bases. We find the necessary and sufficient conditions for the polynomials Pn(x) to be orthogonal. For the special cases where the sets λn correspond to the classical grids, we find the complete solution to these conditions and observe that it leads to the most general Askey-Wilson polynomials and their special and degenerate classes. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
 The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
 The authors thank the referees and the editors for valuable remarks and suggestions. AZ thanks
 to the Centre de Recherches Math´ematiques (Universit´e de Montr´eal) for hospitality. The authors
 would like to thank S. Tsujimoto for stimulating discussions. The research of LV is supported
 in part by a research grant from the Natural Sciences and Engineering Research Council
 (NSERC) of Canada. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases Article published earlier |
| spellingShingle | Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases Vinet, L. Zhedanov, A. |
| title | Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases |
| title_full | Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases |
| title_fullStr | Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases |
| title_full_unstemmed | Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases |
| title_short | Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases |
| title_sort | hypergeometric orthogonal polynomials with respect to newtonian bases |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147742 |
| work_keys_str_mv | AT vinetl hypergeometricorthogonalpolynomialswithrespecttonewtonianbases AT zhedanova hypergeometricorthogonalpolynomialswithrespecttonewtonianbases |