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 ArcCosh

 http://functions.wolfram.com/01.26.27.1547.01

 Input Form

 ArcCosh[z] == -ArcTanh[Sqrt[z^2 - 1]/z] /; Element[I z, Reals] && I z > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List["-", RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "z"], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "\[And]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ">", "0"]]]], ")"]]]]]]

 MathML Form

 cosh - 1 ( z ) - tanh - 1 ( z 2 - 1 z ) /; ( z z > 0 ) Condition z -1 z 2 -1 1 2 z -1 z z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], "z"], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ">", "0"]]]]]]]]]]

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

 2003-08-21