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 |
| Теги: |
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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| Резюме: | 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. |
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