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http://functions.wolfram.com/07.23.03.aq12.01
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Hypergeometric2F1[-(23/5), 3, -(3/5), -z] ==
(1/15625) (15625 - 359375 z - 4369770 z^2 - 9481290 z^3 - 5525520 z^4 +
21528 z^(8/5) (39 + 207 z + 322 z^2 + 154 z^3) Log[1 + z^(1/5)] -
21528 (-1)^(3/5) z^(8/5) (39 + 207 z + 322 z^2 + 154 z^3)
Log[1 - (-1)^(1/5) z^(1/5)] - 839592 (-1)^(1/5) z^(8/5)
Log[1 + (-1)^(2/5) z^(1/5)] - 4456296 (-1)^(1/5) z^(13/5)
Log[1 + (-1)^(2/5) z^(1/5)] - 6932016 (-1)^(1/5) z^(18/5)
Log[1 + (-1)^(2/5) z^(1/5)] - 3315312 (-1)^(1/5) z^(23/5)
Log[1 + (-1)^(2/5) z^(1/5)] + 839592 (-1)^(4/5) z^(8/5)
Log[1 - (-1)^(3/5) z^(1/5)] + 4456296 (-1)^(4/5) z^(13/5)
Log[1 - (-1)^(3/5) z^(1/5)] + 6932016 (-1)^(4/5) z^(18/5)
Log[1 - (-1)^(3/5) z^(1/5)] + 3315312 (-1)^(4/5) z^(23/5)
Log[1 - (-1)^(3/5) z^(1/5)] + 839592 (-1)^(2/5) z^(8/5)
Log[1 + (-1)^(4/5) z^(1/5)] + 4456296 (-1)^(2/5) z^(13/5)
Log[1 + (-1)^(4/5) z^(1/5)] + 6932016 (-1)^(2/5) z^(18/5)
Log[1 + (-1)^(4/5) z^(1/5)] + 3315312 (-1)^(2/5) z^(23/5)
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>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 23 </mn> <mn> 5 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 5 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["23", "5"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, 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</mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3315312 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 4 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 5 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 23 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5525520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6932016 </mn> <mo> ⁢ </mo> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 5 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> 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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
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