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 ArcCosh

 http://functions.wolfram.com/01.26.27.1083.01

 Input Form

 ArcCosh[z] == (Sqrt[z - 1]/Sqrt[1 - z]) (Pi/2 - z Sqrt[1/z^2] ArcCsc[Sqrt[1/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["z", " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List["ArcCsc", "[", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 cosh - 1 ( z ) z - 1 1 - z ( π 2 - z 1 z 2 csc - 1 ( 1 z 2 ) ) z z -1 1 2 1 -1 z 1 2 -1 2 -1 -1 z 1 z 2 -1 1 2 1 z 2 -1 1 2 [/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"], "-", RowBox[List["z", " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List["ArcCsc", "[", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], "]"]]]]]], ")"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]

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

 2003-08-21