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http://functions.wolfram.com/08.02.03.0014.01
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EllipticK[1 - z^2]/EllipticK[z^2] == Sqrt[5] /;
z == Sqrt[1/2 - Sqrt[-2 + Sqrt[5]]]
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Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List["EllipticK", "[", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], "]"]], RowBox[List["EllipticK", "[", SuperscriptBox["z", "2"], "]"]]], "\[Equal]", SqrtBox["5"]]], "/;", RowBox[List["z", "\[Equal]", SqrtBox[RowBox[List[FractionBox["1", "2"], "-", SqrtBox[RowBox[List[RowBox[List["-", "2"]], "+", SqrtBox["5"]]]]]]]]]]]]]
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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> <mrow> <mfrac> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ) </mo> </mrow> </mfrac> <mo> ⩵ </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> ⩵ </mo> <msqrt> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> </msqrt> </mrow> </msqrt> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <eq /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -2 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[RowBox[List["EllipticK", "[", RowBox[List["1", "-", SuperscriptBox["z_", "2"]]], "]"]], RowBox[List["EllipticK", "[", SuperscriptBox["z_", "2"], "]"]]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox["5"], "/;", RowBox[List["z", "\[Equal]", SqrtBox[RowBox[List[FractionBox["1", "2"], "-", SqrtBox[RowBox[List[RowBox[List["-", "2"]], "+", SqrtBox["5"]]]]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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