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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 τ functions.

We consider q-Painlevé equations arising from birational representations of the extended affine Weyl groups of A (1) 4-and (A 1 +A 1) (1)-types. We study their hypergeometric solutions on the level of τ functions.

- Nobutaka Nakazono, Seiji Nishioka
- 2012

Solutions to a q-analog of Painlevé III equation of type D Solutions to a q-analog of Painlevé III equation of type D (1) 7 Abstract. This paper deals with a q-analog of Painlevé III equation of type D (1) 7. We study its algebraic function solutions and transcendental function solutions. We construct algebraic function solutions expressed by Laurent… (More)

- James Atkinson, Phil Howes, Nalini Joshi, Nobutaka Nakazono
- J. London Math. Society
- 2016

We consider a q-Painlevé IV equation which is the A (1) 4-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them are expressed by 2 ϕ 1 basic hypergeometric series and the other is given by 2 ψ 2 bilateral basic… (More)

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