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ArcSec






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSec[z] > Representations through equivalent functions > With related functions > Involving tan-1 > Involving sec-1(z) > Involving sec-1(z) and tan-1(2 (z2-1)1/2/-2+z2)





http://functions.wolfram.com/01.18.27.0389.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSec", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[FractionBox[SqrtBox[FractionBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]], SuperscriptBox["z", "2"]]], RowBox[List[SqrtBox[FractionBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]], SuperscriptBox["z", "4"]]], " ", "z"]]], "+", RowBox[List[SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", "z"]], "+", RowBox[List[SqrtBox[FractionBox[RowBox[List[SqrtBox["2"], "-", "z"]], "z"]], " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox["z"], " ", SqrtBox[FractionBox["z", RowBox[List[SqrtBox["2"], "-", "z"]]]]]], "-", RowBox[List[SqrtBox[RowBox[List["-", FractionBox["1", "z"]]]], " ", SqrtBox[RowBox[List["-", "z"]]], " ", SqrtBox[RowBox[List["-", FractionBox["z", RowBox[List[SqrtBox["2"], "+", "z"]]]]]], " ", SqrtBox[RowBox[List["-", FractionBox[RowBox[List[SqrtBox["2"], "+", "z"]], "z"]]]]]]]], ")"]]]], "+", FractionBox[RowBox[List["2", " ", SqrtBox[SuperscriptBox["z", "2"]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["2", " ", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]]], RowBox[List[RowBox[List["-", "2"]], "+", SuperscriptBox["z", "2"]]]], "]"]]]], "z"]]], ")"]]]]]]]]]]










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





2003-08-21