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EllipticK






Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticK[z] > Specific values > Singular values





http://functions.wolfram.com/08.02.03.0026.01









  


  










Input Form





EllipticK[1 - z^2]/EllipticK[z^2] == Sqrt[17] /; z == 1/Sqrt[(2 + 4 Sqrt[-412 - 100 Sqrt[17] + 5 Sqrt[13598 + 3298 Sqrt[17]]])/ (1649 + 400 Sqrt[17] - 20 Sqrt[13598 + 3298 Sqrt[17]])]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox[RowBox[List["EllipticK", "[", RowBox[List["1", "-", SuperscriptBox["z", "2"]]], "]"]], RowBox[List["EllipticK", "[", SuperscriptBox["z", "2"], "]"]]], "\[Equal]", SqrtBox["17"]]], "/;", RowBox[List["z", "\[Equal]", FractionBox["1", SqrtBox[FractionBox[RowBox[List["2", "+", RowBox[List["4", " ", SqrtBox[RowBox[List[RowBox[List["-", "412"]], "-", RowBox[List["100", " ", SqrtBox["17"]]], "+", RowBox[List["5", " ", SqrtBox[RowBox[List["13598", "+", RowBox[List["3298", " ", SqrtBox["17"]]]]]]]]]]]]]]], RowBox[List["1649", "+", RowBox[List["400", " ", SqrtBox["17"]]], "-", RowBox[List["20", " ", SqrtBox[RowBox[List["13598", "+", RowBox[List["3298", " ", SqrtBox["17"]]]]]]]]]]]]]]]]]]]










MathML Form







<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> &#8289; </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> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> ) </mo> </mrow> </mfrac> <mo> &#10869; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#10869; </mo> <mstyle fontfamily='Times'> <mfrac> <mn> 1 </mn> <msqrt> <mfrac> <mrow> <mn> 2 </mn> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> - </mo> <mn> 412 </mn> </mrow> <mo> - </mo> <mrow> <mn> 100 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 13598 </mn> <mo> + </mo> <mrow> <mn> 3298 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> </mrow> </msqrt> </mrow> </mrow> </msqrt> </mrow> </mrow> <mrow> <mn> 1649 </mn> <mo> + </mo> <mrow> <mn> 400 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 13598 </mn> <mo> + </mo> <mrow> <mn> 3298 </mn> <mo> &#8290; </mo> <msqrt> <mn> 17 </mn> </msqrt> </mrow> </mrow> </msqrt> </mrow> </mrow> </mfrac> </msqrt> </mfrac> </mstyle> </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'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <eq /> <ci> z </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> -412 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 100 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 13598 </cn> <apply> <times /> <cn type='integer'> 3298 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1649 </cn> <apply> <times /> <cn type='integer'> 400 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 13598 </cn> <apply> <times /> <cn type='integer'> 3298 </cn> <apply> <power /> <cn type='integer'> 17 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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["17"], "/;", RowBox[List["z", "\[Equal]", FractionBox["1", SqrtBox[FractionBox[RowBox[List["2", "+", RowBox[List["4", " ", SqrtBox[RowBox[List[RowBox[List["-", "412"]], "-", RowBox[List["100", " ", SqrtBox["17"]]], "+", RowBox[List["5", " ", SqrtBox[RowBox[List["13598", "+", RowBox[List["3298", " ", SqrtBox["17"]]]]]]]]]]]]]]], RowBox[List["1649", "+", RowBox[List["400", " ", SqrtBox["17"]]], "-", RowBox[List["20", " ", SqrtBox[RowBox[List["13598", "+", RowBox[List["3298", " ", SqrtBox["17"]]]]]]]]]]]]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2002-12-18