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

[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.

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