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http://functions.wolfram.com/07.23.03.0987.01
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Hypergeometric2F1[-(11/2), 3, 9/2, z] == (1/(1572864 z^(7/2)))
(Sqrt[z] (17325 -
z (25410 + z (48510 + z (-1264182 + 11 z (335644 +
3 z (-151674 + 35 z (3174 + 13 z (-94 + 15 z)))))))) +
3465 (-1 + z)^7 (5 + 13 z (2 + 5 z)) ArcTanh[Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "3", ",", FractionBox["9", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["1572864", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List["17325", "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List["25410", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["48510", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1264182"]], "+", RowBox[List["11", " ", "z", " ", RowBox[List["(", RowBox[List["335644", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "151674"]], "+", RowBox[List["35", " ", "z", " ", RowBox[List["(", RowBox[List["3174", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "94"]], "+", RowBox[List["15", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SqrtBox["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> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ; </mo> <mfrac> <mn> 9 </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["11", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["9", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric2F1] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1572864 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3465 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 17325 </mn> <mo> - </mo> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 35 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 94 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3174 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 151674 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 335644 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1264182 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 48510 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 25410 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='integer'> 3 </cn> <cn type='rational'> 9 <sep /> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1572864 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3465 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <times /> <apply> <power /> <ci> tanh </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 17325 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 35 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> z </ci> </apply> <cn type='integer'> -94 </cn> </apply> </apply> <cn type='integer'> 3174 </cn> </apply> </apply> <cn type='integer'> -151674 </cn> </apply> </apply> <cn type='integer'> 335644 </cn> </apply> </apply> <cn type='integer'> -1264182 </cn> </apply> </apply> <cn type='integer'> 48510 </cn> </apply> </apply> <cn type='integer'> 25410 </cn> </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["11", "2"]]], ",", "3", ",", FractionBox["9", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List["17325", "-", RowBox[List["z", " ", RowBox[List["(", RowBox[List["25410", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["48510", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1264182"]], "+", RowBox[List["11", " ", "z", " ", RowBox[List["(", RowBox[List["335644", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "151674"]], "+", RowBox[List["35", " ", "z", " ", RowBox[List["(", RowBox[List["3174", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "94"]], "+", RowBox[List["15", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["1572864", " ", SuperscriptBox["z", RowBox[List["7", "/", "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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