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variants of this functions
ArcTan




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[z] > Representations through equivalent functions > With related functions > Involving sech-1 > Involving tan-1(z2/1-z21/2) > Involving tan-1(z2/1-z21/2) and sech-1(1/z)





http://functions.wolfram.com/01.14.27.2780.01









  


  








Input Form





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








Standard Form





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MathML Form







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Rule Form





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


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





2003-08-21