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)}

We present the τ-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 {}_8W_7. By using the W(D_5) symmetry of the function {}_8W_7, we construct a set of twelve solutions and descr...

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Bibliographic Details
Main Author: Tetsu Masuda
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2009-03-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
q-Painlevé system
q-hypergeometric function
Weyl group
τ-function
Online Access:http://dx.doi.org/10.3842/SIGMA.2009.035
Description
Summary:We present the τ-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 {}_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 ~W(D_6^{(1)}) on the set.
ISSN:1815-0659

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