The Ramanujan Journal

, Volume 24, Issue 1, pp 1-31

First online:

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

  • T. MasudaAffiliated withDepartment of Physics and Mathematics, Aoyama Gakuin University Email author 

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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.


q-Painlevé system Rahmann’s q-hypergeometric integral Weyl group τ-function

Mathematics Subject Classification (2000)

33D15 33D05 33D60 33E17