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 ArcCoth

 http://functions.wolfram.com/01.28.27.2828.01

 Input Form

 ArcCoth[z] == -ArcCsch[Sqrt[1 - z^2]/z] + (Pi I)/2 /; Element[z, Reals] && z < -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCoth", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["ArcCsch", "[", FractionBox[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "z"], "]"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]], ")"]]]]]]

 MathML Form

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

 Rule Form

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

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

 2003-09-04