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 ArcCoth

 http://functions.wolfram.com/01.28.27.1824.01

 Input Form

 ArcCoth[Sqrt[-1 - z]/Sqrt[1 - z]] == (I/2) ArcSec[1/z] /; Im[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]], SqrtBox[RowBox[List["1", "-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["ArcSec", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]

 MathML Form

 coth - 1 ( - 1 - z 1 - z ) 2 sec - 1 ( 1 z ) /; Im ( z ) > 0 Condition -1 -1 z 1 2 1 -1 z 1 2 -1 2 -1 1 z -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z_"]]], SqrtBox[RowBox[List["1", "-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["ArcSec", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]]]]]]]]

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

 2003-09-04