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 ArcCosh

 http://functions.wolfram.com/01.26.27.1737.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["z", RowBox[List["z", "-", "1"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], SqrtBox[RowBox[List["-", "z"]]], SqrtBox[FractionBox["1", "z"]]]], "+", RowBox[List[SqrtBox["z"], SqrtBox[FractionBox["1", "z"]], RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]]]]]]]]

 MathML Form

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

 Rule Form

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

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

 2003-08-21