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 Tanh

 http://functions.wolfram.com/01.21.27.0028.01

 Input Form

 Tanh[z] == (Sqrt[z^2]/z) (1/Sqrt[1 - Csc[I z]^2]) /; Re[z] != 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Tanh", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[SqrtBox[SuperscriptBox["z", "2"]], RowBox[List["z", " "]]], FractionBox["1", RowBox[List[" ", SqrtBox[RowBox[List["1", "-", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "2"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[NotEqual]", "0"]]]]]]

 MathML Form

 tanh ( z ) z 2 z 1 1 - csc 2 ( z ) /; Re ( z ) 0 Condition z z 2 1 2 z -1 1 1 -1 z 2 1 2 -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Tanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SqrtBox[SuperscriptBox["z", "2"]], RowBox[List["z", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox[RowBox[List["Csc", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "2"]]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[NotEqual]", "0"]]]]]]]]

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

 2001-10-29