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 ArcCos

 http://functions.wolfram.com/01.13.16.0018.01

 Input Form

 ArcCos[I z] == Pi/2 + (1/2) ArcCos[1 + 2 z^2] /; Inequality[0, Less, Arg[z], LessEqual, Pi]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcCos", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "+", RowBox[List[FractionBox["1", "2"], RowBox[List["ArcCos", "[", RowBox[List["1", "+", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]], "]"]]]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

 MathML Form

 cos - 1 ( z ) 1 2 cos - 1 ( 2 z 2 + 1 ) + π 2 /; 0 < arg ( z ) π Condition z 1 2 2 z 2 1 2 -1 Inequality 0 z [/itex]

 Rule Form

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

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

 2003-08-21