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http://functions.wolfram.com/10.08.17.0020.01
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PolyLog[2, z] == -PolyLog[2, z/(z - 1)] - (1/2) Log[z - 1]^2 + Pi^2/2 -
2 Pi I Log[z] + Pi I Log[z - 1] /; z > 1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox["z", RowBox[List["z", "-", "1"]]]]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], SuperscriptBox[RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]], "2"]]], "+", FractionBox[SuperscriptBox["\[Pi]", "2"], "2"], "-", RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]]]]]]]], "/;", RowBox[List["z", ">", "1"]]]]]]
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<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> <mn> 2 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mfrac> <mi> z </mi> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> > </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <apply> <ln /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <pi /> <apply> <ln /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <imaginaryi /> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <gt /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["PolyLog", "[", RowBox[List["2", ",", FractionBox["z", RowBox[List["z", "-", "1"]]]]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]], "2"]]], "+", FractionBox[SuperscriptBox["\[Pi]", "2"], "2"], "-", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["z", "-", "1"]], "]"]]]]]], "/;", RowBox[List["z", ">", "1"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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