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 ArcCoth

 http://functions.wolfram.com/01.28.27.0748.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04