Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾
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 actio...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149150 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862574637058097152 |
|---|---|
| author | Masuda, T. |
| author_facet | Masuda, T. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-26T10:11:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149150 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T10:11:26Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Masuda, T. 2019-02-19T17:41:58Z 2019-02-19T17:41:58Z 2009 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. 1815-0659 2000 Mathematics Subject Classification: 33D15; 33D05; 33D60; 33E17 https://nasplib.isofts.kiev.ua/handle/123456789/149150 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾ Article published earlier |
| spellingShingle | Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾ Masuda, T. |
| title | Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾ |
| title_full | Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾ |
| title_fullStr | Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾ |
| title_full_unstemmed | Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾ |
| title_short | Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾ |
| title_sort | hypergeometric τ-functions of the q-painlevé system of type e₇⁽¹⁾ |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149150 |
| work_keys_str_mv | AT masudat hypergeometricτfunctionsoftheqpainlevesystemoftypee71 |