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 ArcCosh

 http://functions.wolfram.com/01.26.27.1147.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21