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 ArcCoth

 http://functions.wolfram.com/01.28.27.0448.01

 Input Form

 ArcCoth[z] == I ArcCos[z/Sqrt[z^2 - 1]] - Pi I /; Pi/2 < Arg[z] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", FractionBox["z", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]], "-", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 coth - 1 ( z ) cos - 1 ( z z 2 - 1 ) - π /; π 2 < arg ( z ) < π Condition z z z 2 -1 1 2 -1 -1 2 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", FractionBox["z", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]], "-", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-09-04