Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Type $(A_2+A_1)^{(1)}$

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 $\tau$ functions.