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 ArcSinh

 http://functions.wolfram.com/01.25.27.1907.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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