, Volume 24, Issue 1, pp 1-31

Hypergeometric τ-functions of the q-Painlevé system of type $E_{8}^{(1)}$

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Abstract

We present the τ-functions for the hypergeometric solutions to the q-Painlevé system of type $E_{8}^{(1)}$ in a determinant formula whose entries are given by Rahman’s q-hypergeometric integrals. By using the symmetry of the q-hypergeometric integral, we can construct 56 solutions and describe the action of $W(E_{7}^{(1)})$ on the solutions.