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We consider a $q$-Painlev\'e III equation and a $q$-Painlev\'e II equationarising 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.

Hypergeometric $\tau$ Function of the $q$-Painlev\'e Systems of Type $(A_2+A_1)^{(1)}$