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 ArcTan

 http://functions.wolfram.com/01.14.16.0144.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21

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