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 ArcCosh

 http://functions.wolfram.com/01.26.27.1426.01

 Input Form

 ArcCosh[z] == (Sqrt[z - 1]/Sqrt[1 - z]) (Pi/2 + (Sqrt[-z^2]/z) ArcSinh[Sqrt[-z^2]])

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21