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By using the contiguity operators, we give a simple and elementary derivation of sufficient conditions that Appell’s hypergeometric systems for F2, F3 and F4 are reducible.

kyushu journal of mathematics

REDUCIBILITY OF THE SYSTEMS OF DIFFERENTIAL EQUATIONS SATISFIED BY APPELL'S &lt;b&gt;&lt;i&gt;F&lt;/i&gt;&lt;/b&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;b&gt;&lt;i&gt;,F&lt;/i&gt;&lt;/b&gt;&lt;sub&gt;3 &lt;/sub&gt;AND &lt;b&gt;&lt;i&gt;F&lt;/i&gt;&lt;/b&gt;&lt;sub&gt;4 &lt;/sub&gt;