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 ArcCoth

 http://functions.wolfram.com/01.28.27.0243.01

 Input Form

 ArcCoth[1/Sqrt[z]] == (-((2 Sqrt[-z^2])/z)) ArcSin[Sqrt[(Sqrt[1 - z] - 1)/(2 Sqrt[1 - z])]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox["1", SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], "z"]]], RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "-", "1"]], RowBox[List["2", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], "]"]]]]]]]]

 MathML Form

 coth - 1 ( 1 z ) - 2 - z 2 z sin - 1 ( 1 - z - 1 2 1 - z ) 1 z 1 2 -1 -1 2 -1 z 2 1 2 z -1 1 -1 z 1 2 -1 2 1 -1 z 1 2 -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], "-", "1"]], RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]]]], "]"]]]], "z"]]]]]]]

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

 2003-09-04