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http://functions.wolfram.com/07.23.03.4451.01
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Hypergeometric2F1[5, 6, -(5/2), z] == (1/(32768 (-1 + z)^14))
((-1 + z) (-32768 +
z (819200 + z (-13172736 + z (317128704 +
z (3176160285 + 2 z (2746217091 + 4 z (310755421 +
2 z (15740143 + 72072 z)))))))) -
765765 Sqrt[1 - z] z^(7/2) (1287 + 8 z (715 + 4 z (195 + 4 z (15 + z))))
ArcSin[Sqrt[z]])
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["5", ",", "6", ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["32768", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "14"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "32768"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["819200", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "13172736"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["317128704", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3176160285", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2746217091", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["310755421", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["15740143", "+", RowBox[List["72072", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["765765", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1287", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["715", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["195", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["15", "+", "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> 5 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 5 </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["5", 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["5", "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> 32768 </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> <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> <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> 4 </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> 72072 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 15740143 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 310755421 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2746217091 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3176160285 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 317128704 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 13172736 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 819200 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 32768 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 765765 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <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> <mn> 4 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 195 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 715 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1287 </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> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 5 </cn> <cn type='integer'> 6 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 32768 </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 /> <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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 72072 </cn> <ci> z </ci> </apply> <cn type='integer'> 15740143 </cn> </apply> </apply> <cn type='integer'> 310755421 </cn> </apply> </apply> <cn type='integer'> 2746217091 </cn> </apply> </apply> <cn type='integer'> 3176160285 </cn> </apply> </apply> <cn type='integer'> 317128704 </cn> </apply> </apply> <cn type='integer'> -13172736 </cn> </apply> </apply> <cn type='integer'> 819200 </cn> </apply> </apply> <cn type='integer'> -32768 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 765765 </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'> 7 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> 15 </cn> </apply> </apply> <cn type='integer'> 195 </cn> </apply> </apply> <cn type='integer'> 715 </cn> </apply> </apply> <cn type='integer'> 1287 </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> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["5", ",", "6", ",", RowBox[List["-", FractionBox["5", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "32768"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["819200", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "13172736"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["317128704", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["3176160285", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["2746217091", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["310755421", "+", RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List["15740143", "+", RowBox[List["72072", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["765765", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1287", "+", RowBox[List["8", " ", "z", " ", RowBox[List["(", RowBox[List["715", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["195", "+", RowBox[List["4", " ", "z", " ", RowBox[List["(", RowBox[List["15", "+", "z"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]], RowBox[List["32768", " ", 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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