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variants of this functions
PolyLog






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > PolyLog[2,z] > General characteristics > Symmetries and periodicities > Mirror symmetry





http://functions.wolfram.com/10.07.04.0002.01









  


  










Input Form





PolyLog[2, Conjugate[z]] == Conjugate[PolyLog[2, z]] /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["Conjugate", "[", "z", "]"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]










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> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mstyle scriptlevel='0'> <mn> 2 </mn> </mstyle> </msub> <mo> ( </mo> <mstyle scriptlevel='0'> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mstyle> <mo> ) </mo> </mrow> <mstyle scriptlevel='0'> <mo> &#10869; </mo> </mstyle> <mover> <mstyle scriptlevel='0'> <semantics> <mrow> <msub> <mi> Li </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[InterpretationBox[&quot;Li&quot;, PolyLog, Rule[Editable, False], Rule[Selectable, False]], &quot;2&quot;], RowBox[List[&quot;(&quot;, &quot;z&quot;, &quot;)&quot;]]]], StirlingS1] </annotation> </semantics> </mstyle> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mstyle scriptlevel='0'> <mn> 2 </mn> </mstyle> </msub> <mo> ( </mo> <mstyle scriptlevel='0'> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mstyle> <mo> ) </mo> </mrow> <mstyle scriptlevel='0'> <mo> &#10869; </mo> </mstyle> <mover> <mstyle scriptlevel='0'> <semantics> <mrow> <msub> <mi> Li </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubscriptBox[InterpretationBox[&quot;Li&quot;, PolyLog, Rule[Editable, False], Rule[Selectable, False]], &quot;2&quot;], RowBox[List[&quot;(&quot;, &quot;z&quot;, &quot;)&quot;]]]], StirlingS1] </annotation> </semantics> </mstyle> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["Conjugate", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]], "]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]










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





2001-10-29