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 ArcCoth

 http://functions.wolfram.com/01.28.27.1475.01

 Input Form

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

 Standard Form

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

 MathML Form

 coth - 1 ( 1 1 - z 2 ) csc - 1 ( z ) + π 2 /; π 2 < arg ( z ) < π Condition 1 1 -1 z 2 -1 1 2 z 2 -1 2 -1 z [/itex]

 Rule Form

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

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

 2003-09-04