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 Csch

 http://functions.wolfram.com/01.23.27.0052.01

 Input Form

 Csch[z] == Sqrt[Coth[z]^2 - 1] /; Abs[Im[z]] < Pi/2 && Re[z] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Csch", "[", "z", "]"]], "\[Equal]", " ", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["Coth", "[", "z", "]"]], "2"], "-", "1"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "<", FractionBox["\[Pi]", "2"]]], "\[And]", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]

 MathML Form

 csch ( z ) coth 2 ( z ) - 1 /; "\[LeftBracketingBar]" Im ( z ) "\[RightBracketingBar]" < π 2 Re ( z ) > 0 Condition z z 2 -1 1 2 z 2 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Csch", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["Coth", "[", "z", "]"]], "2"], "-", "1"]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "<", FractionBox["\[Pi]", "2"]]], "&&", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]]]

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

 2001-10-29