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 ArcCosh

 http://functions.wolfram.com/01.26.27.1332.01

 Input Form

 ArcCosh[Sqrt[1 - z]/Sqrt[-z]] == (-I) (Pi/2 - ArcSec[Sqrt[z]]) /; Im[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCosh", "[", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], SqrtBox[RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", " ", RowBox[List["ArcSec", "[", SqrtBox["z"], "]"]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

 cosh - 1 ( 1 - z - z ) - ( π 2 - sec - 1 ( z ) ) /; Im ( z ) < 0 Condition 1 -1 z 1 2 -1 z 1 2 -1 -1 2 -1 -1 z 1 2 z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", FractionBox[SqrtBox[RowBox[List["1", "-", "z_"]]], SqrtBox[RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List["ArcSec", "[", SqrtBox["z"], "]"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-08-21