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arXiv · 1602.01573

A reformulation of the generalized $q$-Painlevé VI system with $W(A^{(1)}_{2n+1})$ symmetry

Takao Suzuki
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Abstract

In the previous work we introduced the higher order $q$-Painlevé system $q$-$P_{(n+1,n+1)}$ as a generalization of the Jimbo-Sakai's $q$-Painlevé VI equation. It is derived from a $q$-analogue of the Drinfeld-Sokolov hierarchy of type $A^{(1)}_{2n+1}$ and admits a particular solution in terms of the Heine's $q$-hypergeometric function ${}_{n+1}ϕ_n$. However the obtained system is insufficient as a generalization of $q$-$P_{\rm{VI}}$ due to some reasons. In this article we rewrite the system $q$-$P_{(n+1,n+1)}$ to a more suitable one.

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Takao Suzuki. 2016-12-24. A reformulation of the generalized $q$-Painlevé VI system with $W(A^{(1)}_{2n+1})$ symmetry. https://arxiv.org/abs/1602.01573

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