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 ArcCoth

 http://functions.wolfram.com/01.28.06.0014.01

 Input Form

 ArcCoth[z] == Sum[z^(-2 k - 1)/(2 k + 1), {k, 0, Infinity}] /; Abs[z] > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", "z", "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[" ", SuperscriptBox["z", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "-", "1"]]]]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]

 MathML Form

 coth - 1 ( z ) k = 0 z - 2 k - 1 2 k + 1 /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" > 1 Condition z k 0 z -2 k -1 2 k 1 -1 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[SuperscriptBox["z", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "-", "1"]]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]]]

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

 2001-10-29