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Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases
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- Фізико-технічні та математичні науки
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- Відділення математики
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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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Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases
Інший ID:
2010 Mathematics Subject Classification: 42C05; 42C15
DOI:10.3842/SIGMA.2016.048
DOI:10.3842/SIGMA.2016.048
Посилання:
Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases / L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 20 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 thank the referees and the editors for valuable remarks and suggestions. AZ thanks
to the Centre de Recherches Math´ematiques (Universit´e de Montr´eal) for hospitality. The authors
would like to thank S. Tsujimoto for stimulating discussions. The research of LV is supported
in part by a research grant from the Natural Sciences and Engineering Research Council
(NSERC) of Canada.
Дата:
2016
Переглядів:
571
Завантажень:
269
Анотація:
We introduce the notion of ''hypergeometric'' polynomials with respect to Newtonian bases. We find the necessary and sufficient conditions for the polynomials Pn(x) to be orthogonal. For the special cases where the sets λn correspond to the classical grids, we find the complete solution to these conditions and observe that it leads to the most general Askey-Wilson polynomials and their special and degenerate classes.
