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 Coth

 http://functions.wolfram.com/01.22.27.0016.01

 Input Form

 Coth[z] == -((I Cos[I z])/Sqrt[1 - Cos[I z]^2]) /; 0 < Im[z] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Coth", "[", "z", "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cos", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "2"]]]]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Im", "[", "z", "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 coth ( z ) - cos ( z ) 1 - cos 2 ( z ) /; 0 < Im ( z ) < π Condition z -1 z 1 -1 z 2 1 2 -1 0 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cos", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "2"]]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Im", "[", "z", "]"]], "<", "\[Pi]"]]]]]]]]

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

 2001-10-29