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 ArcCoth

 http://functions.wolfram.com/01.28.27.2127.01

 Input Form

 ArcCoth[1/Sqrt[z]] == 2 ArcSinh[Sqrt[1 - Sqrt[1 - z]]/(Sqrt[2] (1 - z)^(1/4))]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCoth", "[", FractionBox["1", SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List["2", RowBox[List["ArcSinh", "[", FractionBox[SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]], RowBox[List[SqrtBox["2"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]], "]"]]]]]]]]

 MathML Form

 coth - 1 ( 1 z ) 2 sinh - 1 ( 1 - 1 - z 2 1 - z 4 ) 1 z 1 2 -1 2 1 -1 1 -1 z 1 2 1 2 2 1 2 1 -1 z 1 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCoth", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["2", " ", RowBox[List["ArcSinh", "[", FractionBox[SqrtBox[RowBox[List["1", "-", SqrtBox[RowBox[List["1", "-", "z"]]]]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]], "]"]]]]]]]]

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

 2003-09-04