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 ArcCoth

 http://functions.wolfram.com/01.28.27.3480.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04