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періодичних видань НАН України
періодичних видань НАН України
Classes of Bivariate Orthogonal Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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| dc.contributor.author | Ismail, M.E.H. | |
| dc.contributor.author | Zhang, R. | |
| dc.date.accessioned | 2019-02-14T18:08:54Z | |
| dc.date.available | 2019-02-14T18:08:54Z | |
| dc.date.issued | 2016 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2010 Mathematics Subject Classification: 33C50; 33D50; 33C45; 33D45 | |
| dc.identifier.other | DOI:10.3842/SIGMA.2016.021 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/147415 | |
| dc.description.abstract | 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. | uk_UA |
| dc.description.sponsorship | 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. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | Classes of Bivariate Orthogonal Polynomials | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
