, Volume 24, Issue 1, pp 1-31
Date: 24 Nov 2010

Hypergeometric τ -functions of the q -Painlevé system of type \(E_{8}^{(1)}\)

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.