Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation
We consider a q-Painlevé IV equation which is the A₄⁽¹⁾-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them are expressed by ₂φ₁ basic hypergeometric series a...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146608 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation / N. Nakazono // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862667754088169472 |
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| author | Nakazono, N. |
| author_facet | Nakazono, N. |
| citation_txt | Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation / N. Nakazono // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider a q-Painlevé IV equation which is the A₄⁽¹⁾-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them are expressed by ₂φ₁ basic hypergeometric series and the other is given by ₂ψ₂ bilateral basic hypergeometric series.
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| first_indexed | 2025-12-07T15:23:54Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146608 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:23:54Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
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| spelling | Nakazono, N. 2019-02-10T09:57:23Z 2019-02-10T09:57:23Z 2014 Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation / N. Nakazono // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D05; 33D15; 33D45; 33E17; 39A13 DOI:10.3842/SIGMA.2014.090 https://nasplib.isofts.kiev.ua/handle/123456789/146608 We consider a q-Painlevé IV equation which is the A₄⁽¹⁾-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them are expressed by ₂φ₁ basic hypergeometric series and the other is given by ₂ψ₂ bilateral basic hypergeometric series. The author would like to thank Professors K. Kajiwara, S. Kakei, H. Miki, M. Noumi, and
 S. Tsujimoto for the useful comments. He also appreciates the valuable comments from the
 referees which have improved the quality of this paper. This work has been supported by JSPS
 Grant-in-Aid for Scientific Research No. 22·4366 and the Australian Research Council grant
 DP130100967. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation Article published earlier |
| spellingShingle | Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation Nakazono, N. |
| title | Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation |
| title_full | Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation |
| title_fullStr | Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation |
| title_full_unstemmed | Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation |
| title_short | Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation |
| title_sort | hypergeometric solutions of the a₄⁽¹⁾-surface q-painlevé iv equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146608 |
| work_keys_str_mv | AT nakazonon hypergeometricsolutionsofthea41surfaceqpainleveivequation |