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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147415 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |