Classes of Bivariate Orthogonal Polynomials
We introduce a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-D Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the 2-D Hermite polynomials and a two variable extension of the Zer...
Збережено в:
| Дата: | 2016 |
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| 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/123456789/147415 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Classes of Bivariate Orthogonal Polynomials / M.E.H. Ismail, R. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 39 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147415 |
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dspace |
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irk-123456789-1474152019-02-15T01:25:38Z Classes of Bivariate Orthogonal Polynomials Ismail, M.E.H. Zhang, R. We introduce a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-D Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the 2-D Hermite polynomials and a two variable extension of the Zernike or disc polynomials. We also give q-analogues of all these extensions. In each case in addition to generating functions and three term recursions we provide raising and lowering operators and show that the polynomials are eigenfunctions of second-order partial differential or q-difference operators. 2016 Article Classes of Bivariate Orthogonal Polynomials / M.E.H. Ismail, R. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 39 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C50; 33D50; 33C45; 33D45 DOI:10.3842/SIGMA.2016.021 http://dspace.nbuv.gov.ua/handle/123456789/147415 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 a class of orthogonal polynomials in two variables which generalizes the disc polynomials and the 2-D Hermite polynomials. We identify certain interesting members of this class including a one variable generalization of the 2-D Hermite polynomials and a two variable extension of the Zernike or disc polynomials. We also give q-analogues of all these extensions. In each case in addition to generating functions and three term recursions we provide raising and lowering operators and show that the polynomials are eigenfunctions of second-order partial differential or q-difference operators. |
| format |
Article |
| author |
Ismail, M.E.H. Zhang, R. |
| spellingShingle |
Ismail, M.E.H. Zhang, R. Classes of Bivariate Orthogonal Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ismail, M.E.H. Zhang, R. |
| author_sort |
Ismail, M.E.H. |
| title |
Classes of Bivariate Orthogonal Polynomials |
| title_short |
Classes of Bivariate Orthogonal Polynomials |
| title_full |
Classes of Bivariate Orthogonal Polynomials |
| title_fullStr |
Classes of Bivariate Orthogonal Polynomials |
| title_full_unstemmed |
Classes of Bivariate Orthogonal Polynomials |
| title_sort |
classes of bivariate orthogonal polynomials |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147415 |
| citation_txt |
Classes of Bivariate Orthogonal Polynomials / M.E.H. Ismail, R. Zhang // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 39 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT ismailmeh classesofbivariateorthogonalpolynomials AT zhangr classesofbivariateorthogonalpolynomials |
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2023-05-20T17:27:48Z |
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2023-05-20T17:27:48Z |
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