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 ArcCosh

 http://functions.wolfram.com/01.26.16.0058.01

 Input Form

 ArcCosh[Sqrt[(1 - z)/2]] == (Pi I)/2 - (1/2) ArcCosh[z] /; Element[z, Reals] && -1 < z < 1

 Standard Form

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

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox[RowBox[List["1", "-", "z_"]], "2"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", FractionBox[RowBox[List["ArcCosh", "[", "z", "]"]], "2"]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["-", "1"]], "<", "z", "<", "1"]]]]]]]]]]

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

 2003-08-21