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 ArcCoth

 http://functions.wolfram.com/01.28.27.0665.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-09-04