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EllipticLog




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticLog[{z1,z2},{a,b}] > General characteristics > Symmetries and periodicities > Mirror symmetry





http://functions.wolfram.com/09.57.04.0002.01









  


  








Input Form





EllipticLog[{Conjugate[Subscript[z, 1]], Conjugate[Subscript[z, 2]]}, {Conjugate[a], Conjugate[b]}] == Conjugate[EllipticLog[{Subscript[z, 1], Subscript[z, 2]}, {a, b}]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["Conjugate", "[", SubscriptBox["z", "1"], "]"]], ",", RowBox[List["Conjugate", "[", SubscriptBox["z", "2"], "]"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Conjugate", "[", "a", "]"]], ",", RowBox[List["Conjugate", "[", "b", "]"]]]], "}"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> elog </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mover> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> <mo> , </mo> <mrow> <mover> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <mi> a </mi> <mo> _ </mo> </mover> </mrow> <mo> , </mo> <mover> <mi> b </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <semantics> <mrow> <mi> elog </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mi> a </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;elog&quot;, &quot;(&quot;, RowBox[List[SubscriptBox[&quot;z&quot;, &quot;1&quot;], &quot;,&quot;, RowBox[List[SubscriptBox[&quot;z&quot;, &quot;2&quot;], &quot;;&quot;, &quot;a&quot;]], &quot;,&quot;, &quot;b&quot;]], &quot;)&quot;]], BernoulliB] </annotation> </semantics> <mo> _ </mo> </mover> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> elog </ci> <apply> <ci> OverBar </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> OverBar </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> OverBar </ci> <ci> a </ci> </apply> </apply> <apply> <ci> OverBar </ci> <ci> b </ci> </apply> </apply> <apply> <ci> OverBar </ci> <apply> <ci> BernoulliB </ci> <apply> <ci> elog </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["Conjugate", "[", SubscriptBox["z_", "1"], "]"]], ",", RowBox[List["Conjugate", "[", SubscriptBox["z_", "2"], "]"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["Conjugate", "[", "a_", "]"]], ",", RowBox[List["Conjugate", "[", "b_", "]"]]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Conjugate", "[", RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["zz", "1"], ",", SubscriptBox["zz", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]], "]"]]]]]]


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





2001-10-29