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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.

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Masuda, T. Hypergeometric τ-functions of the q-Painlevé system of type \(E_{8}^{(1)}\) . Ramanujan J 24, 1–31 (2011). https://doi.org/10.1007/s11139-010-9262-1

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