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 Coth

 http://functions.wolfram.com/01.22.27.0076.01

 Input Form

 Coth[z] == (Sqrt[-z^2]/z) (1/Sqrt[Sech[z]^2 - 1]) /; Abs[Im[z]] < Pi/2

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2001-10-29