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http://functions.wolfram.com/08.02.03.0021.01
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EllipticK[1 - z^2]/EllipticK[z^2] == Sqrt[12] /;
z == Sqrt[833 - 340 Sqrt[6] - 12 Sqrt[9602 - 3920 Sqrt[6]]]
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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["12"]]], "/;", RowBox[List["z", "\[Equal]", SqrtBox[RowBox[List["833", "-", RowBox[List["340", " ", SqrtBox["6"]]], "-", RowBox[List["12", " ", SqrtBox[RowBox[List["9602", "-", RowBox[List["3920", " ", SqrtBox["6"]]]]]]]]]]]]]]]]]
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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> 12 </mn> </msqrt> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> ⩵ </mo> <msqrt> <mrow> <mn> 833 </mn> <mo> - </mo> <mrow> <mn> 340 </mn> <mo> ⁢ </mo> <msqrt> <mn> 6 </mn> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 9602 </mn> <mo> - </mo> <mrow> <mn> 3920 </mn> <mo> ⁢ </mo> <msqrt> <mn> 6 </mn> </msqrt> </mrow> </mrow> </msqrt> </mrow> </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'> 12 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <eq /> <ci> z </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 833 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 340 </cn> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 9602 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3920 </cn> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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["12"], "/;", RowBox[List["z", "\[Equal]", SqrtBox[RowBox[List["833", "-", RowBox[List["340", " ", SqrtBox["6"]]], "-", RowBox[List["12", " ", SqrtBox[RowBox[List["9602", "-", RowBox[List["3920", " ", SqrtBox["6"]]]]]]]]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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