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 ArcSinh

 http://functions.wolfram.com/01.25.27.1909.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21