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 ArcCoth

 http://functions.wolfram.com/01.28.27.2677.01

 Input Form

 ArcCoth[z] == (-((Pi I)/2)) Sign[Im[z]] + ArcTanh[z] /; Im[z] != 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], " ", RowBox[List["Sign", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], "+", RowBox[List["ArcTanh", "[", "z", "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[NotEqual]", "0"]]]]]]

 MathML Form

 coth - 1 ( z ) tanh - 1 ( z ) - π 2 sgn ( Im ( z ) ) /; Im ( z ) 0 Condition z z -1 2 -1 Sign z z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["-", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]], ")"]], " ", RowBox[List["Sign", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], "+", RowBox[List["ArcTanh", "[", "z", "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[NotEqual]", "0"]]]]]]]]

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

 2003-09-04