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 ArcSinh

 http://functions.wolfram.com/01.25.27.1976.01

 Input Form

 ArcSinh[Sqrt[z^2 - 1]/Sqrt[-z^2]] == -ArcSech[z] - Pi I /; Pi/2 < Arg[z] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcSinh", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", RowBox[List["ArcSech", "[", "z", "]"]]]], "-", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 sinh - 1 ( z 2 - 1 - z 2 ) - sech - 1 ( z ) - π /; π 2 < arg ( z ) < π Condition z 2 -1 1 2 -1 z 2 1 2 -1 -1 z -1 2 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSinh", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]], SqrtBox[RowBox[List["-", SuperscriptBox["z_", "2"]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["ArcSech", "[", "z", "]"]]]], "-", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-08-21