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 ArcCosh

 http://functions.wolfram.com/01.26.27.0614.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21