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 ArcCosh

 http://functions.wolfram.com/01.26.27.0301.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21