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variants of this functions
PolyLog




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > PolyLog[2,z] > Series representations > Generalized power series > Expansions at z==1 > For the function itself





http://functions.wolfram.com/10.07.06.0007.02









  


  








Input Form





PolyLog[2, z] \[Proportional] Pi^2/6 + O[z - 1] - Log[1 - z] (z - 1) (1 + O[z - 1])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "6"], "+", RowBox[List["O", "[", RowBox[List["z", "-", "1"]], "]"]], "-", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]], RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "-", "1"]], "]"]]]], ")"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <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> &#8733; </mo> <mrow> <mfrac> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mn> 6 </mn> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <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["PolyLog", "[", RowBox[List["2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "6"], "+", RowBox[List["O", "[", RowBox[List["z", "-", "1"]], "]"]], "-", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", "z"]], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "-", "1"]], "]"]]]], ")"]]]]]]]]]]


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





2001-10-29