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 ArcCosh

 http://functions.wolfram.com/01.26.27.0652.01

 Input Form

 ArcCosh[Sqrt[z^2]/Sqrt[z^2 + 1]] == (Pi I)/2 - I ArcTan[z] /; 0 <= Arg[z] <= Pi/2

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21