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http://functions.wolfram.com/07.23.03.b5fv.01
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Hypergeometric2F1[-(47/8), 27/8, 2, z] ==
(16 2^(1/4) (-2 Sqrt[1 - z] (9148503 - 812454638 z + 5687085119 z^2 -
14876318520 z^3 + 18476749200 z^4 - 11068599360 z^5 + 2584108800 z^6)
EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] -
Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (9148503 - 812454638 z +
5687085119 z^2 - 14876318520 z^3 + 18476749200 z^4 - 11068599360 z^5 +
2584108800 z^6) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] +
Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (9148503 - 812454638 z +
5687085119 z^2 - 14876318520 z^3 + 18476749200 z^4 - 11068599360 z^5 +
2584108800 z^6) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] +
Sqrt[1 - Sqrt[1 - z]])] + (9148503 + 376850752 z - 5709620261 z^2 +
24302721790 z^3 - 47662327440 z^4 + 48495851040 z^5 - 24979718400 z^6 +
5168217600 z^7) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] +
Sqrt[1 - Sqrt[1 - z]])]))/(9560185635 Pi
Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z)
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["47", "8"]]], ",", FractionBox["27", "8"], ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["16", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["9148503", "-", RowBox[List["812454638", " ", "z"]], "+", RowBox[List["5687085119", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["14876318520", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18476749200", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["11068599360", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2584108800", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["2", "-", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["9148503", "-", RowBox[List["812454638", " ", "z"]], "+", RowBox[List["5687085119", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["14876318520", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18476749200", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["11068599360", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2584108800", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["9148503", "-", RowBox[List["812454638", " ", "z"]], "+", RowBox[List["5687085119", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["14876318520", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18476749200", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["11068599360", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["2584108800", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["9148503", "+", RowBox[List["376850752", " ", "z"]], "-", RowBox[List["5709620261", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["24302721790", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["47662327440", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["48495851040", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["24979718400", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["5168217600", " ", SuperscriptBox["z", "7"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["9560185635", " ", "\[Pi]", " ", SqrtBox[RowBox[List[SqrtBox["2"], "+", SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]], " ", "z"]], ")"]]]]]]]]
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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> 47 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 27 </mn> <mn> 8 </mn> </mfrac> </mrow> <mo> ; </mo> <mn> 2 </mn> <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["47", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["27", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], 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</mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2584108800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 11068599360 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 18476749200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14876318520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5687085119 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 812454638 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 9148503 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </msqrt> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2584108800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 11068599360 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 18476749200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14876318520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5687085119 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 812454638 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 9148503 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </msqrt> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2584108800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 11068599360 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 18476749200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14876318520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5687085119 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 812454638 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 9148503 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </msqrt> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5168217600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 24979718400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 48495851040 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 47662327440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 24302721790 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5709620261 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 376850752 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 9148503 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </msqrt> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 9560185635 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msqrt> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </msqrt> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </msqrt> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 47 <sep /> 8 </cn> </apply> <cn type='rational'> 27 <sep /> 8 </cn> </list> <list> <cn type='integer'> 2 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2584108800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11068599360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 18476749200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14876318520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5687085119 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 812454638 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 9148503 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn 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Date Added to functions.wolfram.com (modification date)
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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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