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variants of this functions
EllipticE




Mathematica Notation

Traditional Notation









Elliptic Integrals > EllipticE[z] > Identities > Functional identities





http://functions.wolfram.com/08.01.17.0003.01









  


  








Input Form





EllipticE[z] == Sqrt[1 - z] Conjugate[EllipticE[z/(z - 1)]] /; Element[z, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["EllipticE", "[", "z", "]"]], "\[Equal]", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], RowBox[List["Conjugate", "[", RowBox[List["EllipticE", "[", FractionBox["z", RowBox[List["z", "-", "1"]]], "]"]], "]"]]]]]], "/;", RowBox[List["z", "\[Element]", "Reals"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <mover> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[List[], Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> EllipticE </ci> <ci> z </ci> </apply> <apply> <times /> <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> <ci> OverBar </ci> <apply> <ci> EllipticE </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> z </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticE", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["Conjugate", "[", RowBox[List["EllipticE", "[", FractionBox["z", RowBox[List["z", "-", "1"]]], "]"]], "]"]]]], "/;", RowBox[List["z", "\[Element]", "Reals"]]]]]]]]


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





2007-05-02