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 ArcCoth

 http://functions.wolfram.com/01.28.27.0732.01

 Input Form

 ArcCoth[(1/z) Sqrt[z^2/(1 - z^2)]] == (-I) ArcCos[1/z] /; 0 <= Arg[z] <= Pi/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", RowBox[List[FractionBox["1", "z"], SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["ArcCos", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 coth - 1 ( 1 z z 2 1 - z 2 ) - cos - 1 ( 1 z ) /; 0 arg ( z ) π 2 Condition 1 z -1 z 2 1 -1 z 2 -1 1 2 -1 1 z -1 0 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[FractionBox[SuperscriptBox["z_", "2"], RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]]], "z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["ArcCos", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2003-09-04