Nakazono, Nobutaka Hypergeometric \(\tau \) functions of the \(q\)-Painlevé systems of type \((A_{2}+A_{1})^{(1)}\). (English) Zbl 1217.33027 SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 084, 16 p. (2010). Summary: We consider a \(q\)-Painlevé III equation and a \(q\)-Painlevé II equation arising from a birational representation of the affine Weyl group of type \((A_{2}+A_{1})^{(1)}\). We study their hypergeometric solutions on the level of \(\tau \) functions. Cited in 2 Documents MSC: 33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals 33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\) 33E17 Painlevé-type functions 39A13 Difference equations, scaling (\(q\)-differences) Keywords:\(q\)-Painlevé system; hypergeometric function; affine Weyl group; \(\tau \) function PDFBibTeX XMLCite \textit{N. Nakazono}, SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 084, 16 p. (2010; Zbl 1217.33027) Full Text: DOI arXiv