A reformulation of the generalized q-Painlevé VI system with W(A⁽¹⁾₂ₙ₊₁) symmetry

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₊₁φₙ|⁠. However, the obtained system is insufficient as a generalization of |q|-|PVI| due to some reasons. In this article, we rewrite the system |q|-|P(n+1,n+1)| to a more suitable one.