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 (2)

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

Cited by in corpus (9)

• Geometric Aspects of Painlevé Equations
• Hypergeometric Solutions for the $q$-Painlevé Equation of type $E_6^{(1)}$ by Padé Method
• Hypergeometric $\tau$ Function of the $q$-Painlevé Systems of Type $(A_2+A_1{)}^{(1)}$
• The Padé interpolation method applied to $q$-Painlevé equations
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case
• A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$
• Lens Generalisation of $\tau$-functions for the Elliptic Discrete Painlevé Equation
• Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$
• Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation