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KleinInvariantJ




Mathematica Notation

Traditional Notation









Elliptic Functions > KleinInvariantJ[z] > Specific values > Values at fixed points > Values at quadratic irrationalities (Heegner Numbers)





http://functions.wolfram.com/09.50.03.0005.01









  


  








Input Form





KleinInvariantJ[(1 + I Sqrt[7])/2] == -(125/64)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["KleinInvariantJ", "[", FractionBox[RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]]]], "2"], "]"]], "\[Equal]", RowBox[List["-", FractionBox["125", "64"]]]]]]]








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> J </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mn> 7 </mn> </msqrt> </mrow> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;J&quot;, &quot;(&quot;, FractionBox[RowBox[List[&quot;1&quot;, &quot;+&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, SqrtBox[&quot;7&quot;]]]]], &quot;2&quot;], &quot;)&quot;]], InterpretTemplate[Function[KleinInvariantJ[Slot[1]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 125 </mn> <mn> 64 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <semantics> <mrow> <mi> J </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mn> 7 </mn> </msqrt> </mrow> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;J&quot;, &quot;(&quot;, FractionBox[RowBox[List[&quot;1&quot;, &quot;+&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, SqrtBox[&quot;7&quot;]]]]], &quot;2&quot;], &quot;)&quot;]], InterpretTemplate[Function[KleinInvariantJ[Slot[1]]]]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 125 </mn> <mn> 64 </mn> </mfrac> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KleinInvariantJ", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]]]], ")"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox["125", "64"]]]]]]]


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





2001-10-29