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 ArcTan

 http://functions.wolfram.com/01.14.16.0039.01

 Input Form

 ArcTan[Sqrt[z^2]] == -(Pi/2) + ArcTan[1/z] /; Element[I z, Reals] && 0 < I z < 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTan", "[", SqrtBox[SuperscriptBox["z", "2"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "+", RowBox[List["ArcTan", "[", FractionBox["1", "z"], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "\[And]", RowBox[List["0", "<", RowBox[List["\[ImaginaryI]", " ", "z"]], "<", "1"]]]], ")"]]]]]]

 MathML Form

 tan - 1 ( z 2 ) tan - 1 ( 1 z ) - π 2 /; ( z 0 < z < 1 ) Condition z 2 1 2 1 z -1 -1 2 -1 z 0 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTan", "[", SqrtBox[SuperscriptBox["z_", "2"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "+", RowBox[List["ArcTan", "[", FractionBox["1", "z"], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "\[Element]", "Reals"]], "&&", RowBox[List["0", "<", RowBox[List["\[ImaginaryI]", " ", "z"]], "<", "1"]]]]]]]]]]

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

 2003-08-21