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 ArcCosh

 http://functions.wolfram.com/01.26.27.1321.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21