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 ArcCoth

 http://functions.wolfram.com/01.28.27.0033.02

 Input Form

 ArcCoth[z] == (-((Pi z)/2)) Sqrt[-(1/z^2)] Sqrt[1/(1 - z^2)] Sqrt[1 - z^2] + ArcTanh[z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCoth", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "z"]], "2"]]], SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], SqrtBox[FractionBox["1", RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], "+", RowBox[List["ArcTanh", "[", "z", "]"]]]]]]]]

 MathML Form

 coth - 1 ( z ) tanh - 1 ( z ) - π z 2 - 1 z 2 1 1 - z 2 1 - z 2 z z -1 z 2 -1 -1 1 z 2 -1 1 2 1 1 -1 z 2 -1 1 2 1 -1 z 2 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["\[Pi]", " ", "z"]], ")"]]]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]], " ", SqrtBox[FractionBox["1", RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]], "+", RowBox[List["ArcTanh", "[", "z", "]"]]]]]]]]

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

 2001-10-29