This article is cited in 6 papers

Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Type $(A_2+A_1)^{(1)}$

Nobutaka Nakazono

Graduate School of Mathematics, Kyushu University, 744 Motooka, Fukuoka, 819-0395, Japan

Abstract: 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.

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

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

Received: August 17, 2010; in final form October 8, 2010; Published online October 14, 2010

Language: English

DOI: 10.3842/SIGMA.2010.084

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ArXiv: 1008.2595