A higher order Painlevé system in two variables and extensions of the Appell hypergeometric functions $F_1$, $F_2$ and $F_3$

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 differential equations.

20 pages, to be published in "Funkcialaj Ekvacioj"

References in corpus (2)

• A Particular Solution of a Painlevé System in Terms of the Hypergeometric Function ${}_{n+1}{F}_n$
• Six-dimensional Painleve systems and their particular solutions in terms of hypergeometric functions