Hypergeometric $\tau$-Functions of the $q$-Painlevé System of Type $E_7^{(1)}$

Abstract

We present the $\tau$-functions for the hypergeometric solutions to the $q$-Painlevé system of type $E_7^{(1)}$ in a determinant formula whose entries are given by the basic hypergeometric function ${}_8{W}_7$. By using the $W(D_5)$ symmetry of the function ${}_8{W}_7$, we construct a set of twelve solutions and describe the action of $\tilde{W}(D_6^{(1)})$ on the set.

References in corpus (1)

• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$

Cited by in corpus (2)

• Hypergeometric $\tau$ Function of the $q$-Painlevé Systems of Type $(A_2+A_1{)}^{(1)}$
• A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$