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 ArcCoth

 http://functions.wolfram.com/01.28.27.1461.01

 Input Form

 ArcCoth[Sqrt[(z - 1)/(z + 1)]] == (I/2) ArcCsc[1/z] + (Pi I)/4 /; Im[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", SqrtBox[FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["z", "+", "1"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["ArcCsc", "[", FractionBox["1", "z"], "]"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 coth - 1 ( z - 1 z + 1 ) 1 2 csc - 1 ( 1 z ) + π 4 /; Im ( z ) < 0 Condition z -1 z 1 -1 1 2 1 2 1 z -1 4 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", SqrtBox[FractionBox[RowBox[List["z_", "-", "1"]], RowBox[List["z_", "+", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["ArcCsc", "[", FractionBox["1", "z"], "]"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-09-04