Hypergeometric Solutions of the A₄⁽¹⁾-Surface q-Painlevé IV Equation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2014
• Main Author: Nakazono, N.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146608
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...