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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2016 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2016
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147415 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862706661958877184 |
|---|---|
| author | Ismail, M.E.H. Zhang, R. |
| author_facet | Ismail, M.E.H. Zhang, R. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T17:00:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147415 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:00:55Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ismail, M.E.H. Zhang, R. 2019-02-14T18:08:54Z 2019-02-14T18:08:54Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/147415 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. 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 are very grateful to the anonymous referees for their detailed reports on the first
 draft of this paper. Research of M.E.H. Ismail supported by a grant from DSFP program at
 King Saud and by the National Plan for Science, Technology and innovation (MAARIFAH),
 King Abdelaziz City for Science and Technology, Kingdom of Saudi Arabia, Award number
 14-MAT623-02. Research of R. Zhang partially supported by National Science Foundation of
 China, grant No. 11371294. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Classes of Bivariate Orthogonal Polynomials Article published earlier |
| spellingShingle | Classes of Bivariate Orthogonal Polynomials Ismail, M.E.H. Zhang, R. |
| title | 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_short | Classes of Bivariate Orthogonal Polynomials |
| title_sort | classes of bivariate orthogonal polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147415 |
| work_keys_str_mv | AT ismailmeh classesofbivariateorthogonalpolynomials AT zhangr classesofbivariateorthogonalpolynomials |