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 Coth

 http://functions.wolfram.com/01.22.16.0020.01

 Input Form

 Coth[(I ArcCsc[z])/2] == (-((I Sqrt[z^2])/z)) (Sqrt[z^2] + Sqrt[z^2 - 1])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Coth", "[", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCsc", "[", "z", "]"]]]], "2"], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", SqrtBox[SuperscriptBox["z", "2"]], " "]], "z"]]], RowBox[List["(", RowBox[List[SqrtBox[SuperscriptBox["z", "2"]], "+", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]], ")"]]]]]]]]

 MathML Form

 coth ( 2 csc - 1 ( z ) ) - z 2 z ( z 2 + z 2 - 1 ) 2 -1 z -1 z 2 1 2 z -1 z 2 1 2 z 2 -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["ArcCsc", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SqrtBox[SuperscriptBox["z", "2"]]]], ")"]], " ", RowBox[List["(", RowBox[List[SqrtBox[SuperscriptBox["z", "2"]], "+", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]], ")"]]]], "z"]]]]]]]

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

 2001-10-29