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SIGMA, 2016, Volume 12, 051, 23 pages (Mi sigma1133)  

Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1')^{(1)}$

Nobutaka Nakazono

School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia

Abstract: We consider $q$-Painlevé equations arising from birational representations of the extended affine Weyl groups of $A_4^{(1)}$- and $(A_1+A_1)^{(1)}$-types. We study their hypergeometric solutions on the level of $\tau$ functions.

Keywords: $q$-Painlevé equation; basic hypergeometric function; affine Weyl group; $\tau$ function.

Funding Agency Grant Number
Australian Research Council DP130100967
This research was supported by grant # DP130100967 from the Australian Research Council.


DOI: https://doi.org/10.3842/SIGMA.2016.051

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Full text: http://www.emis.de/journals/SIGMA/2016/051/
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Bibliographic databases:

ArXiv: 1601.05327
MSC: 33D05; 33D15; 33E17; 39A13
Received: February 1, 2016; in final form May 16, 2016; Published online May 20, 2016
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Citation: Nobutaka Nakazono, “Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1')^{(1)}$”, SIGMA, 12 (2016), 051, 23 pp.

Citation in format AMSBIB
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\by Nobutaka~Nakazono
\paper Hypergeometric $\tau$ Functions of the $q$-Painlev\'e Systems of Types $A_4^{(1)}$ and $(A_1+A_1')^{(1)}$
\jour SIGMA
\yr 2016
\vol 12
\papernumber 051
\totalpages 23
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\crossref{https://doi.org/10.3842/SIGMA.2016.051}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84975082478}


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