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arXiv · 1602.04573

A higher order Painlev\'e system in two variables and extensions of the Appell hypergeometric functions $F_1$, $F_2$ and $F_3$

Takao Suzuki
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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 Painlev\'e 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.

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Takao Suzuki. 2016-02-15. A higher order Painlev\'e system in two variables and extensions of the Appell hypergeometric functions $F_1$, $F_2$ and $F_3$. https://arxiv.org/abs/1602.04573

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