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 ArcCosh

 http://functions.wolfram.com/01.26.27.0258.01

 Input Form

 ArcCosh[Sqrt[z]] == (-I) ArcCos[Sqrt[z]] /; Im[z] < 0 || (Element[z, Reals] && z > 1)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["ArcCos", "[", SqrtBox["z"], "]"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", ">", "1"]]]], ")"]]]]]]]]

 MathML Form

 cosh - 1 ( z ) - cos - 1 ( z ) /; Im ( z ) < 0 ( z z > 1 ) Condition z 1 2 -1 z 1 2 z 0 z z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["ArcCos", "[", SqrtBox["z"], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]], "||", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", ">", "1"]]]], ")"]]]]]]]]]]

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

 2003-08-21