A Higher Order Painlevé System in Two Variables and Extensions of the Appell Hypergeometric Functions F₁, F₂ and F₃

抄録

In this article we propose an extension of Appell hypergeometric function F₂ (or equivalently F₃). It is derived from a particular solution of a higher order Painlevé system in two variables. On the other hand, an extension of Appell's F₁ was introduced by Tsuda. We also show that those two extensions are equivalent at the level of systems of linear partial differential equations.