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 PolyLog

 http://functions.wolfram.com/10.07.21.0002.01

 Input Form

 Integrate[PolyLog[2, z], z] == Sum[z^(k + 1)/((k + 1) k^2), {k, 1, Infinity}] /; Abs[z] < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox["z", RowBox[List["k", "+", "1"]]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], SuperscriptBox["k", "2"]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]

 MathML Form

 Li PolyLog 2 ( z ) z k = 1 z k + 1 ( k + 1 ) k 2 /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 Condition z PolyLog 2 z k 1 z k 1 k 1 k 2 -1 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["PolyLog", "[", RowBox[List["2", ",", "z_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "\[Infinity]"], FractionBox[SuperscriptBox["z", RowBox[List["k", "+", "1"]]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], " ", SuperscriptBox["k", "2"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]

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

 2001-10-29