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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 cosh-1 > Involving tan-1(1/z2-11/2) > Involving tan-1(1/z2-11/2) and cosh-1(1/z)





http://functions.wolfram.com/01.14.27.1870.01









  


  








Input Form





ArcTan[Sqrt[1/(z^2 - 1)]] == (-Sqrt[-1 - z]) Sqrt[-(1/z^4)] z^2 Sqrt[-(1/(1 + z))] ArcCosh[1/z] + Sqrt[1/(z^2 - 1)] Sqrt[z^2 - 1] (-1 + Sqrt[(z - 1)/(z + 1)] Sqrt[(z + 1)/(z - 1)] + Sqrt[z^2]/z) (Pi/2)








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["1", RowBox[List[SuperscriptBox["z_", "2"], "-", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]]]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SuperscriptBox["z", "4"]]]]], " ", SuperscriptBox["z", "2"], " ", SqrtBox[RowBox[List["-", FractionBox["1", RowBox[List["1", "+", "z"]]]]]], " ", RowBox[List["ArcCosh", "[", FractionBox["1", "z"], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SqrtBox[FractionBox["1", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], " ", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List[SqrtBox[FractionBox[RowBox[List["z", "-", "1"]], RowBox[List["z", "+", "1"]]]], " ", SqrtBox[FractionBox[RowBox[List["z", "+", "1"]], RowBox[List["z", "-", "1"]]]]]], "+", FractionBox[SqrtBox[SuperscriptBox["z", "2"]], "z"]]], ")"]], " ", "\[Pi]"]]]]]]]]


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





2003-08-21