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ModularLambda




Mathematica Notation

Traditional Notation









Elliptic Functions > ModularLambda[z] > Identities > Functional identities





http://functions.wolfram.com/09.51.17.0003.01









  


  








Input Form





ModularLambda[z] == 1 - ModularLambda[-(1/z)]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ModularLambda", "[", "z", "]"]], "\[Equal]", RowBox[List["1", "-", RowBox[List["ModularLambda", "[", RowBox[List["-", FractionBox["1", "z"]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mi> &#955; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Lambda]&quot;, &quot;(&quot;, TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> &#955; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Lambda]&quot;, &quot;(&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[&quot;1&quot;, &quot;z&quot;]]], Rule[Editable, True]], &quot;)&quot;]], InterpretTemplate[Function[ModularLambda[Slot[1]]]]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> ModularLambda </ci> <ci> z </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> ModularLambda </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ModularLambda", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "-", RowBox[List["ModularLambda", "[", RowBox[List["-", FractionBox["1", "z"]]], "]"]]]]]]]]


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





2001-10-29