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 ArcCosh

 http://functions.wolfram.com/01.26.27.2314.01

 Input Form

 ArcCosh[z] == 2 ArcSech[Sqrt[2/(1 + z)]] /; !IntervalMemberQ[Interval[{-Infinity, -1}], z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List["2", " ", RowBox[List["ArcSech", "[", SqrtBox[FractionBox["2", RowBox[List["1", "+", "z"]]]], "]"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", " ", "z"]], "]"]], "]"]]]]]]

 MathML Form

 cosh - 1 ( z ) 2 sech - 1 ( 2 1 + z ) /; ​​ z ( - , - 1 ) cosh - 1 ( z ) 2 sech - 1 ( 2 1 + z ) /; ​​ z ( - , - 1 ) [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", RowBox[List["ArcSech", "[", SqrtBox[FractionBox["2", RowBox[List["1", "+", "z"]]]], "]"]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]

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

 2003-08-21