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 ArcCoth

 http://functions.wolfram.com/01.28.27.0451.01

 Input Form

 ArcCoth[z] == (-I) ArcCos[Sqrt[z^2]/Sqrt[z^2 - 1]] /; Inequality[0, LessEqual, Arg[z], Less, Pi]

 Standard Form

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

 MathML Form

 coth - 1 ( z ) - cos - 1 ( z 2 z 2 - 1 ) /; 0 arg ( z ) < π Condition z -1 z 2 1 2 z 2 -1 1 2 -1 Inequality 0 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[SqrtBox[SuperscriptBox["z", "2"]], SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]], "/;", RowBox[List["0", "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-09-04