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 PolyLog

 http://functions.wolfram.com/10.08.20.0001.01

 Input Form

 D[PolyLog[\[Nu], z], \[Nu]] == -Sum[(Log[k] z^k)/k^\[Nu], {k, 2, Infinity}] /; Abs[z] < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "\[Nu]"], RowBox[List["PolyLog", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", " ", RowBox[List["-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "2"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["Log", "[", "k", "]"]], SuperscriptBox["z", "k"]]], SuperscriptBox["k", "\[Nu]"]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["\[Nu]_"]]], RowBox[List["PolyLog", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "2"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["Log", "[", "k", "]"]], " ", SuperscriptBox["z", "k"]]], SuperscriptBox["k", "\[Nu]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]

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

 2001-10-29