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 Csch

 http://functions.wolfram.com/01.23.16.0019.01

 Input Form

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

 Standard Form

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

 MathML Form

 csch ( 2 cot - 1 ( z ) ) - 1 z 2 2 z 1 - 1 1 + 1 z 2 2 -1 z -1 1 z 2 -1 1 2 2 1 2 z 1 -1 1 1 1 z 2 -1 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["ArcCot", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]], ")"]]]], SqrtBox[RowBox[List["1", "-", FractionBox["1", SqrtBox[RowBox[List["1", "+", FractionBox["1", SuperscriptBox["z", "2"]]]]]]]]]]]]]]]]

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

 2001-10-29