Hypergeometric $τ$ Function of the $q$ -Painlevé Systems of Type $(A_2+A_1)^{(1)}$

preprint2010arXivOpen access

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.

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Hypergeometric $τ$ Function of the $q$ -Painlevé Systems of Type $(A_2+A_1)^{(1)}$

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Hypergeometric τττ Function of the qqq-Painlevé Systems of Type (A2+A1)(1)(A_2+A_1)^{(1)}(A2​+A1​)(1)

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Hypergeometric $τ$ Function of the $q$ -Painlevé Systems of Type $(A_2+A_1)^{(1)}$