We consider a q-Painlevé III equation and a q-Painlevé II equation arising from a birational representation of the affine Weyl group of type (A 2 + A 1) (1). We study their hypergeometric solutions on the level of τ functions.
We consider a q-Painlevé IV equation which is the A (1) 4-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 ϕ 1 basic hypergeometric series and the other is given by 2 ψ 2 bilateral basic… (More)