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 ArcCosh

 http://functions.wolfram.com/01.26.16.0040.01

 Input Form

 ArcCosh[2 z^2 - 1] == -2 ArcCosh[z] + 2 Pi I /; Element[z, Reals] && -1 < z < 0

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", RowBox[List[RowBox[List["2", " ", SuperscriptBox["z_", "2"]]], "-", "1"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["ArcCosh", "[", "z", "]"]]]], "+", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", 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