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variants of this functions
PolyLog




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > PolyLog[2,z] > Representations through more general functions > Through hypergeometric functions of two variables





http://functions.wolfram.com/10.07.26.0004.01









  


  








Input Form





PolyLog[2, z] == Pi^2/12 + (1/4) (-2 + 1/z)^2 HypergeometricPFQ[{{}, {1, 1}, {1, 1}}, {{3}, {}, {}}, 2 - 1/z, 2 - 1/z] - (1/2) Log[1/z]^2








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "12"], "+", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", FractionBox["1", "z"]]], ")"]], "2"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "1"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "3", "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["2", "-", FractionBox["1", "z"]]], ",", RowBox[List["2", "-", FractionBox["1", "z"]]]]], "]"]]]], "-", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", FractionBox["1", "z"], "]"]], "2"]]]]]]]]]


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





2001-10-29