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 ArcSinh

 http://functions.wolfram.com/01.25.27.1900.01

 Input Form

 ArcSinh[Sqrt[z]] == (Pi I)/2 - ArcSech[1/Sqrt[-z]] /; Element[z, Reals] && -1 < z < 0

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["ArcSech", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "0"]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSinh", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["ArcSech", "[", FractionBox["1", SqrtBox[RowBox[List["-", "z"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "0"]]]]]]]]]]

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

 2003-08-21