Hypergeometric2F1[-(16/5), 5, 9/5, z] == (1/(5859375 z^(4/5))) (5830335 z^(4/5) - 49656880 z^(9/5) + 107987880 z^(14/5) - 67026960 z^(19/5) - 528 (44 - 3696 z + 24024 z^2 - 45136 z^3 + 25389 z^4) Log[1 - z^(1/5)] + 528 (-1)^(1/5) (44 - 3696 z + 24024 z^2 - 45136 z^3 + 25389 z^4) Log[1 + (-1)^(1/5) z^(1/5)] - 23232 (-1)^(2/5) Log[1 - (-1)^(2/5) z^(1/5)] + 1951488 (-1)^(2/5) z Log[1 - (-1)^(2/5) z^(1/5)] - 12684672 (-1)^(2/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] + 23831808 (-1)^(2/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 13405392 (-1)^(2/5) z^4 Log[1 - (-1)^(2/5) z^(1/5)] + 23232 (-1)^(3/5) Log[1 + (-1)^(3/5) z^(1/5)] - 1951488 (-1)^(3/5) z Log[1 + (-1)^(3/5) z^(1/5)] + 12684672 (-1)^(3/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 23831808 (-1)^(3/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] + 13405392 (-1)^(3/5) z^4 Log[1 + (-1)^(3/5) z^(1/5)] - 23232 (-1)^(4/5) Log[1 - (-1)^(4/5) z^(1/5)] + 1951488 (-1)^(4/5) z Log[1 - (-1)^(4/5) z^(1/5)] - 12684672 (-1)^(4/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 23831808 (-1)^(4/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)] - 13405392 (-1)^(4/5) z^4 Log[1 - (-1)^(4/5) z^(1/5)])

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 16 </mn> <mn> 5 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ; </mo> <mfrac> <mn> 9 </mn> <mn> 5 </mn> </mfrac> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, &quot;2&quot;], SubscriptBox[&quot;F&quot;, &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;16&quot;, &quot;5&quot;]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], &quot;,&quot;, TagBox[&quot;5&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[FractionBox[&quot;9&quot;, &quot;5&quot;], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo> &#63449; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 5859375 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> 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2007-05-02