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 ArcCsch

 http://functions.wolfram.com/01.29.27.1869.01

 Input Form

 ArcCsch[Sqrt[(2 Sqrt[1 - z^2])/(1 - Sqrt[1 - z^2])]] == ((z Sqrt[z^(-2)])/2) ArcTanh[z]

 Standard Form

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

 MathML Form

 csch - 1 ( 2 1 - z 2 1 - 1 - z 2 ) z 2 1 z 2 tanh - 1 ( z ) 2 1 -1 z 2 1 2 1 -1 1 -1 z 2 1 2 -1 1 2 z 2 -1 1 z 2 -1 1 2 z [/itex]

 Rule Form

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

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

 2003-08-21