Masuda, Tetsu Hypergeometric \(\tau \)-functions of the \(q\)-Painlevé system of type \(E_{7}^{(1)}\). (English) Zbl 1163.33321 SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 035, 30 p. (2009). Summary: We present the \(\tau \)-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 \(_{8}W_{7}\). By using the \(W(D_{5})\) symmetry of the function \(_{8}W_{7}\), we construct a set of twelve solutions and describe the action of \(^{~}W(D_{6}^{(1)})\) on the set. Cited in 4 Documents MSC: 33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\) 33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals 33D60 Basic hypergeometric integrals and functions defined by them 33E17 Painlevé-type functions Keywords:\(q\)-Painlevé system; \(q\)-hypergeometric function; Weyl group; \(\tau \)-function PDFBibTeX XMLCite \textit{T. Masuda}, SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 035, 30 p. (2009; Zbl 1163.33321) Full Text: DOI arXiv