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Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation
Інший ID:
2010 Mathematics Subject Classification: 33D05; 33D15; 33D45; 33E17; 39A13
DOI:10.3842/SIGMA.2014.090
DOI:10.3842/SIGMA.2014.090
Посилання:
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.
Підтримка:
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.
Дата:
2014
Переглядів:
377
Завантажень:
215
Анотація:
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.
