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 ArcCoth

 http://functions.wolfram.com/01.28.27.0419.01

 Input Form

 ArcCoth[z] == (I/2) (Pi/2 - ArcCos[(2 I z)/(1 - z^2)]) /; Abs[z] > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcCos", "[", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", "z"]], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "]"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]

 MathML Form

 coth - 1 ( z ) 2 ( π 2 - cos - 1 ( 2 z 1 - z 2 ) ) /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" > 1 Condition z 2 -1 2 -1 -1 2 z 1 -1 z 2 -1 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcCos", "[", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", "z"]], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "]"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]]]

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

 2003-09-04