Hypergeometric Solutions of the A 4 (1) -Surface q -Painlevé IV Equation

Symmetry Integrability and Geometry-Methods and Applications

article

Nobutaka Nakazono¹ 

[1] School of Mathematics and Statistics, The University of Sydney

关键词: q-Painlev´e equation;    basic hypergeometric function;    af fine Weyl group;    τ -function;    projective reduction;    orthogonal polynomial;   

DOI  :  10.3842/SIGMA.2014.090

来源: National Academy of Science of Ukraine

【 摘 要 】

We consider a $q$-Painlevé IV equation which is the $A_4^{(1)}$-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 ${}_2\varphi_1$ basic hypergeometric series and the other is given by ${}_2\psi_2$ bilateral basic hypergeometric series.

【 授权许可】

Unknown