A Higher Order Painleve System in Two Variables and Extensions of the Appell Hypergeometric Functions, F-1, F-2 and F-3

作者：Suzum Takao^*

来源：Funkcialaj Ekvacioj-Serio Internacia, 2018, 61(1): 81-107.

DOI：10.1619/fesi.61.81

• Painleve equations
• Isomonodromy deformations
• Hypergeometric functions
• Appell and Lauricella functions

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 Painleve 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 differential equations.

• 出版日期2018-4