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 ArcCoth

 http://functions.wolfram.com/01.28.27.2387.01

 Input Form

 ArcCoth[z] == -2 ArcCosh[Sqrt[(Sqrt[z^2 - 1] - z)/(2 Sqrt[z^2 - 1])]] /; Re[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "2"]], RowBox[List["ArcCosh", "[", SqrtBox[FractionBox[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "-", "z"]], RowBox[List["2", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 coth - 1 ( z ) - 2 cosh - 1 ( z 2 - 1 - z 2 z 2 - 1 ) /; Re ( z ) < 0 Condition z -2 z 2 -1 1 2 -1 z 2 z 2 -1 1 2 -1 1 2 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "-", "z"]], RowBox[List["2", " ", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]]]], "]"]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-09-04