A Higher Order Painlevé System in Two Variables and Extensions of the Appell Hypergeometric Functions <i>F</i>₁, <i>F</i>₂ and <i>F</i>₃

Abstract

Abstract. In this article we propose an extension of Appell hypergeometric function F 2 (or equivalently F 3 ). 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 F 1 was introduced by Tsuda. We also show that those two extensions are equivalent at the level of systems of linear partial di¤erential equations.