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Recurrence Coefficients of a New Generalization of the Meixner Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Recurrence Coefficients of a New Generalization of the Meixner Polynomials
Інший ID:
2010 Mathematics Subject Classification: 34M55; 33E17; 33C47; 42C05; 64Q30
DOI:10.3842/SIGMA.2011.068
DOI:10.3842/SIGMA.2011.068
Посилання:
Recurrence Coefficients of a New Generalization of the Meixner Polynomials / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 12 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html.
GF is partially supported by Polish MNiSzW Grant N N201 397937. WVA is supported by
Belgian Interuniversity Attraction Pole P6/02, FWO grant G.0427.09 and K.U. Leuven Research Grant OT/08/033.
Дата:
2011
Переглядів:
413
Завантажень:
200
Анотація:
We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N+1−β and on the bi-lattice N∪(N+1−β). We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlevé equation PV. Initial conditions for different lattices can be transformed to the classical solutions of PV with special values of the parameters. We also study one property of the Bäcklund transformation of PV.
