, Volume 24, Issue 1, pp 1-31
Date: 24 Nov 2010

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.