Nobutaka Nakazono, “Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1')^{(1)}$”, SIGMA, 2016, Volume 12,051, 23 pp.

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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.

MSC: 33D05; 33D15; 33E17; 39A13

Received: February 1, 2016; in final form May 16, 2016; Published online May 20, 2016

Language: English

DOI: 10.3842/SIGMA.2016.051