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http://functions.wolfram.com/07.23.03.ahlx.01
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Hypergeometric2F1[-(1/4), 11/4, -(11/2), z] ==
(1/(177408 Pi^(3/2)))
(((1/(-1 + z)^8) (2 (44352 - 343728 z + 1155000 z^2 - 2184567 z^3 +
2507340 z^4 - 1702426 z^5 + 389844 z^6 - 149175 z^7 + 21216 z^8)
EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^8)
(2 (44352 - 343728 z + 1155000 z^2 - 2184567 z^3 + 2507340 z^4 -
1702426 z^5 + 389844 z^6 - 149175 z^7 + 21216 z^8)
EllipticE[(1/2) (1 + Sqrt[z])]) +
(1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7))
((-44352 + 22176 Sqrt[z] + 321552 z - 151536 z^(3/2) - 1003464 z^2 +
439362 z^(5/2) + 1745205 z^3 - 694485 z^(7/2) - 1812855 z^4 +
630355 z^(9/2) + 1072071 z^5 - 292383 z^(11/2) - 97461 z^6 +
133263 z^(13/2) + 15912 z^7 - 21216 z^(15/2))
EllipticK[(1/2) (1 - Sqrt[z])]) +
(1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8))
((44352 + 22176 Sqrt[z] - 321552 z - 151536 z^(3/2) + 1003464 z^2 +
439362 z^(5/2) - 1745205 z^3 - 694485 z^(7/2) + 1812855 z^4 +
630355 z^(9/2) - 1072071 z^5 - 292383 z^(11/2) + 97461 z^6 +
133263 z^(13/2) - 15912 z^7 - 21216 z^(15/2))
EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)
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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> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 11 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </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["1", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "4"], 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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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