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Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾
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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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Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾
Інший ID:
2000 Mathematics Subject Classification: 33D15; 33D05; 33D60; 33E17
Посилання:
Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾ / T. Masuda // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 18 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 author would like to express his sincere thanks to Professors M. Noumi and Y. Yamada for valuable discussions and comments. Especially, he owes initial steps of this work, including the formulation by means of the lattice τ -functions and the bilinear equations, to discussions with them. The author would also thank Professors K. Kajiwara and Y. Ohta for stimulating discussions.
Дата:
2009
Переглядів:
389
Завантажень:
259
Анотація:
We present the τ-functions for the hypergeometric solutions to the q-Painlevé system of type E₇⁽¹⁾ in a determinant formula whose entries are given by the basic hypergeometric function ₈W₇. By using the W(D₅) symmetry of the function ₈W₇, we construct a set of twelve solutions and describe the action of ~W(D₆⁽¹⁾) on the set.
