Hypergeometric τ-Functions of the q-Painlevé System of Type E₇⁽¹⁾

Abstract

We present the τ-functions for the hypergeometric solutions to the q-Painlevé system of type E₇⁽¹⁾ in a determinant formula whose entries are given by the basic hypergeometric function ₈W₇. By using the W(D₅) symmetry of the function ₈W₇, we construct a set of twelve solutions and describe the action of ~W(D₆⁽¹⁾) on the set.