Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Classes of Bivariate Orthogonal Polynomials
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
Classes of Bivariate Orthogonal Polynomials
Інший ID:
2010 Mathematics Subject Classification: 33C50; 33D50; 33C45; 33D45
DOI:10.3842/SIGMA.2016.021
DOI:10.3842/SIGMA.2016.021
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
702
Завантажень:
274
Анотація:
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.
