The Ramanujan Journal

, Volume 24, Issue 1, pp 1–31

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


DOI: 10.1007/s11139-010-9262-1

Cite this article as:
Masuda, T. Ramanujan J (2011) 24: 1. doi:10.1007/s11139-010-9262-1


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 systemRahmann’s q-hypergeometric integralWeyl groupτ-function

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Physics and MathematicsAoyama Gakuin UniversityFuchinobeJapan