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 ArcSinh

 http://functions.wolfram.com/01.25.27.1982.01

 Input Form

 ArcSinh[Sqrt[(1 - z^2)/z^2]] == ArcSech[z] + Pi I /; Inequality[Pi/2, LessEqual, Arg[z], Less, Pi]

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21