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 Coth

 http://functions.wolfram.com/01.22.16.0077.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2007-05-02