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 ArcSinh

 http://functions.wolfram.com/01.25.27.1899.01

 Input Form

 ArcSinh[Sqrt[z]] == -((Pi I)/2) + ArcSech[1/Sqrt[-z]] /; Inequality[-Pi, Less, Arg[z], LessEqual, 0]

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "+", RowBox[List["ArcSech", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

 MathML Form

 sinh - 1 ( z ) - π 2 + sech - 1 ( 1 - z ) /; - π < arg ( z ) 0 Condition z 1 2 -1 2 -1 1 -1 z 1 2 -1 Inequality -1 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSinh", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]], "+", RowBox[List["ArcSech", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "0"]]]]]]]]

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

 2003-08-21