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 Csch

 http://functions.wolfram.com/01.23.16.0018.01

 Input Form

 Csch[(I ArcTan[z])/2] == -((I Sqrt[2] Sqrt[z^2])/ (z Sqrt[1 - 1/Sqrt[1 + z^2]]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Csch", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", "z", "]"]]]], "2"], "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SqrtBox[SuperscriptBox["z", "2"]]]], RowBox[List["z", " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]]]]]]]]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Csch", "[", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SqrtBox[SuperscriptBox["z", "2"]]]], RowBox[List["z", " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]]]]]]]]]]]]]]]

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

 2001-10-29