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http://functions.wolfram.com/07.23.03.4516.01
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Hypergeometric2F1[6, 6, -(3/2), z] == (1/(65536 (-1 + z)^14))
((-(-1 + z)) (65536 + z (-2424832 +
z (102629376 + z (1739182875 + 4 z (1245791175 +
z (993610281 + 8 z (27463666 + 1139987 z))))))) +
45045 Sqrt[1 - z] z^(5/2)
(9009 + 2 z (32175 + 16 z (3575 + 2 z (975 + 2 z (75 + 2 z)))))
ArcSin[Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["6", ",", "6", ",", RowBox[List["-", FractionBox["3", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["65536", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "14"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]], " ", RowBox[List["(", RowBox[List["65536", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2424832"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["102629376", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1739182875", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1245791175", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["993610281", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["27463666", "+", RowBox[List["1139987", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["45045", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List["9009", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["32175", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["3575", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["975", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["75", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", 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> <mn> 6 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 3 </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["6", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["3", "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> 65536 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 14 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 45045 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 75 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 975 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3575 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 32175 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 9009 </mn> </mrow> <mo> ) </mo> </mrow> <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> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1139987 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 27463666 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 993610281 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1245791175 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1739182875 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 102629376 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2424832 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 65536 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 6 </cn> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 65536 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 14 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 45045 </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> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> 75 </cn> </apply> </apply> <cn type='integer'> 975 </cn> </apply> </apply> <cn type='integer'> 3575 </cn> </apply> </apply> <cn type='integer'> 32175 </cn> </apply> </apply> <cn type='integer'> 9009 </cn> </apply> <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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <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'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 1139987 </cn> <ci> z </ci> </apply> <cn type='integer'> 27463666 </cn> </apply> </apply> <cn type='integer'> 993610281 </cn> </apply> </apply> <cn type='integer'> 1245791175 </cn> </apply> </apply> <cn type='integer'> 1739182875 </cn> </apply> </apply> <cn type='integer'> 102629376 </cn> </apply> </apply> <cn type='integer'> -2424832 </cn> </apply> </apply> <cn type='integer'> 65536 </cn> </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["6", ",", "6", ",", RowBox[List["-", FractionBox["3", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]], " ", RowBox[List["(", RowBox[List["65536", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2424832"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["102629376", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["1739182875", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["1245791175", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["993610281", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["27463666", "+", RowBox[List["1139987", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["45045", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List["9009", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["32175", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List["3575", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["975", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["75", "+", RowBox[List["2", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["65536", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "14"]]]]]]]] |
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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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