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 ArcCosh

 http://functions.wolfram.com/01.26.16.0123.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21