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 ArcCosh

 http://functions.wolfram.com/01.26.16.0039.01

 Input Form

 ArcCosh[2 z^2 - 1] == 2 ArcCosh[z] + 2 Pi I /; Inequality[-Pi, Less, Arg[z], LessEqual, -(Pi/2)]

 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["2", RowBox[List["ArcCosh", "[", "z", "]"]]]], "+", RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]]]]], "/;", RowBox[List[RowBox[List["-", " ", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

 cosh - 1 ( 2 z 2 - 1 ) 2 cosh - 1 ( z ) + 2 π /; - π < arg ( z ) - π 2 Condition 2 z 2 -1 2 z 2 Inequality -1 z -1 2 -1 [/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["2", " ", RowBox[List["ArcCosh", "[", "z", "]"]]]], "+", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]]]

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

 2003-08-21