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 ArcCsch

 http://functions.wolfram.com/01.29.27.0390.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCsch", "[", FractionBox[SqrtBox["2"], SqrtBox[RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "-", "1"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], RowBox[List["2", " ", "z"]]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcCos", "[", "z", "]"]]]], ")"]]]]]]]]

 MathML Form

 csch - 1 ( 2 1 - z 2 - 1 ) - z 2 2 z ( π 2 - cos - 1 ( z ) ) 2 1 2 1 -1 z 2 1 2 -1 1 2 -1 -1 z 2 1 2 2 z -1 2 -1 -1 z [/itex]

 Rule Form

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

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

 2003-08-21