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 ArcSinh

 http://functions.wolfram.com/01.25.06.0058.01

 Input Form

 ArcSinh[z]^2 == -(Pi/2 - 2 ArcSin[Sqrt[(-(I/2)) (z + I)]])^2

 Standard Form

 Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["ArcSinh", "[", "z", "]"]], "2"], "\[Equal]", RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["2", RowBox[List["ArcSin", "[", SqrtBox[RowBox[List[RowBox[List["-", FractionBox["\[ImaginaryI]", "2"]]], RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]]]]], "]"]]]]]], ")"]], "2"]]]]]]]

 MathML Form

 sinh - 1 ( z ) 2 - ( π 2 - 2 sin - 1 ( - 2 ( z + ) ) ) 2 z 2 -1 2 -1 -1 2 -1 2 -1 z 1 2 2 [/itex]

 Rule Form

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

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

 2007-05-02