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 ArcSinh

 http://functions.wolfram.com/01.25.27.1921.01

 Input Form

 ArcSinh[Sqrt[-z^2]] == Sqrt[(z - 1)/z] Sqrt[z/(z - 1)] ArcSech[1/z] + (Pi Sqrt[-z^2])/(2 z)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSinh", "[", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SqrtBox[FractionBox[RowBox[List["z", "-", "1"]], "z"]], SqrtBox[FractionBox["z", RowBox[List["z", "-", "1"]]]], RowBox[List["ArcSech", "[", FractionBox["1", "z"], "]"]]]], "+", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], RowBox[List["2", "z"]]]]]]]]]

 MathML Form

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

 Rule Form

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

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

 2003-08-21