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 ArcTan

 http://functions.wolfram.com/01.14.16.0027.01

 Input Form

 ArcTan[Sqrt[z]] == (Pi/2) Sqrt[(z + 1)/z] Sqrt[z/(z + 1)] - Sqrt[z] Sqrt[1/z] ArcTan[Sqrt[1/z]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTan", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], "z"]], SqrtBox[FractionBox["z", RowBox[List["z", "+", "1"]]]]]], "-", RowBox[List[SqrtBox["z"], SqrtBox[FractionBox["1", "z"]], RowBox[List["ArcTan", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]]]]]]

 MathML Form

 tan - 1 ( z ) π 2 z + 1 z z z + 1 - z 1 z tan - 1 ( 1 z ) z 1 2 2 -1 z 1 z -1 1 2 z z 1 -1 1 2 -1 z 1 2 1 z -1 1 2 1 z -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTan", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], "z"]], " ", SqrtBox[FractionBox["z", RowBox[List["z", "+", "1"]]]]]], "-", RowBox[List[SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]], " ", RowBox[List["ArcTan", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]]]]]]

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

 2003-08-21