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 ArcSinh

 http://functions.wolfram.com/01.25.27.1860.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21