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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | 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 |
| Цитувати: | 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| id |
nasplib_isofts_kiev_ua-123456789-146608 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation |
| spellingShingle |
Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation Nakazono, N. |
| title_short |
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_sort |
hypergeometric solutions of the a₄⁽¹⁾-surface q-painlevé iv equation |
| author |
Nakazono, N. |
| author_facet |
Nakazono, N. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146608 |
| 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. |
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AT nakazonon hypergeometricsolutionsofthea41surfaceqpainleveivequation |
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2025-12-07T15:23:54Z |
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2025-12-07T15:23:54Z |
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1850863554228387840 |