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http://functions.wolfram.com/07.23.03.5375.01
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Hypergeometric2F1[-(14/3), 11/3, 5/2, z] == (1/(7082725 z^(3/2)))
(27 (-((1/Sqrt[1 - z]) (Sqrt[z] (616 - 246079 z + 1665999 z^2 -
4224584 z^3 + 5127824 z^4 - 3019328 z^5 + 695552 z^6)
Cos[ArcSin[Sqrt[z]]/3])) - (-1848 - 49280 z + 723291 z^2 -
2575560 z^3 + 3878992 z^4 - 2671552 z^5 + 695552 z^6)
Sin[ArcSin[Sqrt[z]]/3]))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["14", "3"]]], ",", FractionBox["11", "3"], ",", FractionBox["5", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["7082725", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List["27", " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", "z"]]]], RowBox[List["(", RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List["616", "-", RowBox[List["246079", " ", "z"]], "+", RowBox[List["1665999", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4224584", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5127824", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3019328", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["695552", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], "3"], "]"]]]], ")"]]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1848"]], "-", RowBox[List["49280", " ", "z"]], "+", RowBox[List["723291", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2575560", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3878992", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2671552", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["695552", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], "3"], "]"]]]]]], ")"]]]], ")"]]]]]]]]
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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> 14 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 11 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mn> 5 </mn> <mn> 2 </mn> </mfrac> <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["14", "3"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "3"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 7082725 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 27 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 695552 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3019328 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5127824 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4224584 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1665999 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 246079 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 616 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 695552 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2671552 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3878992 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2575560 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 723291 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 49280 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1848 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </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'> 14 <sep /> 3 </cn> </apply> <cn type='rational'> 11 <sep /> 3 </cn> </list> <list> <cn type='rational'> 5 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 7082725 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <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> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 695552 </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'> 3019328 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5127824 </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'> 4224584 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1665999 </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'> 246079 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 616 </cn> </apply> <apply> <times /> <ci> cos </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <times /> <apply> <power /> <ci> sin </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 695552 </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'> 2671552 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3878992 </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'> 2575560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 723291 </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'> 49280 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1848 </cn> </apply> <apply> <times /> <ci> sin </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <times /> <apply> <power /> <ci> sin </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["14", "3"]]], ",", FractionBox["11", "3"], ",", FractionBox["5", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["27", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List["616", "-", RowBox[List["246079", " ", "z"]], "+", RowBox[List["1665999", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4224584", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5127824", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["3019328", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["695552", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], "3"], "]"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1848"]], "-", RowBox[List["49280", " ", "z"]], "+", RowBox[List["723291", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2575560", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3878992", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["2671552", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["695552", " ", SuperscriptBox["z", "6"]]]]], ")"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]], "3"], "]"]]]]]], ")"]]]], RowBox[List["7082725", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]]]] |
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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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