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

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

2009-03-24

arxiv.org/abs/0903.4102v1

SIGMA 5 (2009), 035, 30 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.3842/SIGMA.2009.035

We present the $\tau$-functions for the hypergeometric solutions to the
$q$-Painlev\'e system of type $E_7^{(1)}$ in a determinant formula whose
entries are given by the basic hypergeometric function ${}_8W_7$. By using the
$W(D_5)$ symmetry of the function ${}_8W_7$, we construct a set of twelve
solutions and describe the action of $\widetilde{W}(D_6^{(1)})$ on the set.

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