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Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle
Інший ID:
2000 Mathematics Subject Classification: 33E05; 33E30; 33C47
Посилання:
Elliptic Hypergeometric Laurent Biorthogonal Polynomials with a Dense Point Spectrum on the Unit Circle / S. Tsujimoto, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21–25, 2008, MPIM, Bonn, Germany). The authors thank L. Golinskii, A. Kirillov, C. Krattenthaler, A. Magnus, M. Rahman and V. Spiridonov for discussion. The authors are also indebted to the referees for careful reading the manuscript and many suggestions leading to improving of the text.
Дата:
2009
Переглядів:
415
Завантажень:
223
Анотація:
Using the technique of the elliptic Frobenius determinant, we construct new elliptic solutions of the QD-algorithm. These solutions can be interpreted as elliptic solutions of the discrete-time Toda chain as well. As a by-product, we obtain new explicit orthogonal and biorthogonal polynomials in terms of the elliptic hypergeometric function ₃E₂(z). Their recurrence coefficients are expressed in terms of the elliptic functions. In the degenerate case we obtain the Krall-Jacobi polynomials and their biorthogonal analogs.
