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 ArcCosh

 http://functions.wolfram.com/01.26.27.1849.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"]]], "-", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

 cosh - 1 ( z ) - π 2 - coth - 1 ( z 2 - 1 z ) /; - π < arg ( z ) - π 2 Condition z -1 2 -1 -1 z 2 -1 1 2 z -1 Inequality -1 z -1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]]]], "-", RowBox[List["ArcCoth", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "z"], "]"]]]], "/;", 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