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http://functions.wolfram.com/07.23.03.ahpe.01
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Hypergeometric2F1[-(1/4), 15/4, -(11/2), z] ==
(1/(1951488 Pi^(3/2)))
(((1/(-1 + z)^9) (2 (-487872 + 4246704 z - 16275336 z^2 + 35820939 z^3 -
49170924 z^4 + 41563346 z^5 - 12864852 z^6 + 7413003 z^7 -
2110992 z^8 + 254592 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) +
(1/(-1 + z)^9) (2 (-487872 + 4246704 z - 16275336 z^2 + 35820939 z^3 -
49170924 z^4 + 41563346 z^5 - 12864852 z^6 + 7413003 z^7 -
2110992 z^8 + 254592 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) +
(1/((-1 + Sqrt[z])^9 (1 + Sqrt[z])^8))
((487872 - 243936 Sqrt[z] - 4002768 z + 1899744 z^(3/2) + 14375592 z^2 -
6404706 z^(5/2) - 29416233 z^3 + 12102024 z^(7/2) + 37068900 z^4 -
13689500 z^(9/2) - 27873846 z^5 + 8576568 z^(11/2) + 4288284 z^6 -
6002802 z^(13/2) - 1410201 z^7 + 1920048 z^(15/2) + 190944 z^8 -
254592 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) -
(1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^9))
((487872 + 243936 Sqrt[z] - 4002768 z - 1899744 z^(3/2) + 14375592 z^2 +
6404706 z^(5/2) - 29416233 z^3 - 12102024 z^(7/2) + 37068900 z^4 +
13689500 z^(9/2) - 27873846 z^5 - 8576568 z^(11/2) + 4288284 z^6 +
6002802 z^(13/2) - 1410201 z^7 - 1920048 z^(15/2) + 190944 z^8 +
254592 z^(17/2)) 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> 15 </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["15", "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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