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 ArcCosh

 http://functions.wolfram.com/01.26.27.2316.01

 Input Form

 ArcCosh[z] == Pi I (1 - Sqrt[z + 1] Sqrt[1/(z + 1)]) + 2 ArcSech[Sqrt[2/(1 + z)]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCosh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", RowBox[List["(", RowBox[List["1", "-", RowBox[List[SqrtBox[RowBox[List["z", "+", "1"]]], SqrtBox[FractionBox["1", RowBox[List["z", "+", "1"]]]]]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["ArcSech", "[", SqrtBox[FractionBox["2", RowBox[List["1", "+", "z"]]]], "]"]]]]]]]]]]

 MathML Form

 cosh - 1 ( z ) π ( 1 - z + 1 1 z + 1 ) + 2 sech - 1 ( 2 z + 1 ) z 1 -1 z 1 1 2 1 z 1 -1 1 2 2 2 z 1 -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List[SqrtBox[RowBox[List["z", "+", "1"]]], " ", SqrtBox[FractionBox["1", RowBox[List["z", "+", "1"]]]]]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["ArcSech", "[", SqrtBox[FractionBox["2", RowBox[List["1", "+", "z"]]]], "]"]]]]]]]]]]

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

 2003-08-21