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...
Збережено в:
| Дата: | 2016 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147742 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147742 |
|---|---|
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dspace |
| spelling |
irk-123456789-1477422019-02-16T01:25:20Z Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases Vinet, L. Zhedanov, A. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147742 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Vinet, L. Zhedanov, A. |
| spellingShingle |
Vinet, L. Zhedanov, A. Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Vinet, L. Zhedanov, A. |
| author_sort |
Vinet, L. |
| title |
Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases |
| title_short |
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_sort |
hypergeometric orthogonal polynomials with respect to newtonian bases |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147742 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT vinetl hypergeometricorthogonalpolynomialswithrespecttonewtonianbases AT zhedanova hypergeometricorthogonalpolynomialswithrespecttonewtonianbases |
| first_indexed |
2023-05-20T17:28:11Z |
| last_indexed |
2023-05-20T17:28:11Z |
| _version_ |
1796153364801650688 |