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

Abstract

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.