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 ArcSinh

 http://functions.wolfram.com/01.25.27.1920.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21