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 Coth

 http://functions.wolfram.com/01.22.16.0088.01

 Input Form

 Coth[I ArcCsch[z]] == 1/(1 - 2/(1 + (Sqrt[1 + 1/z^2] + 1/z)^(2 I)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCsch", "[", "z", "]"]]]], "]"]], "\[Equal]", FractionBox["1", RowBox[List["1", "-", FractionBox["2", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", FractionBox["1", SuperscriptBox["z", "2"]]]]], "+", FractionBox["1", "z"]]], ")"]], RowBox[List["2", " ", "\[ImaginaryI]"]]]]]]]]]]]]]

 MathML Form

 coth ( csch - 1 ( z ) ) 1 1 - 2 ( 1 + 1 z 2 + 1 z ) 2 + 1 z 1 1 -1 2 1 1 z 2 -1 1 2 1 z -1 2 1 -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCsch", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List["1", "-", FractionBox["2", RowBox[List["1", "+", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", FractionBox["1", SuperscriptBox["z", "2"]]]]], "+", FractionBox["1", "z"]]], ")"]], RowBox[List["2", " ", "\[ImaginaryI]"]]]]]]]]]]]]]

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

 2007-05-02