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ArcSec




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSec[z] > Representations through equivalent functions > With related functions > Involving tanh-1 > Involving sec-1((a2 z2 c-1)1/2/a zc) > Involving sec-1((a2 z2 c-1)1/2/a zc) and tanh-1(a zc)





http://functions.wolfram.com/01.18.27.1710.01









  


  








Input Form





ArcSec[Sqrt[a^2 z^(2 c) - 1]/(a z^c)] == (Pi/2) (1 - Sqrt[1/(a z^c + 1)] Sqrt[a z^c + 1] + Sqrt[1/(1 - a z^c)] Sqrt[1 - a z^c]) + Sqrt[1/(1 - a^2 z^(2 c))] Sqrt[a^2 z^(2 c) - 1] ArcTanh[a z^c]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcSec", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List[SuperscriptBox["a_", "2"], " ", SuperscriptBox["z_", RowBox[List["2", " ", "c_"]]]]], "-", "1"]]], RowBox[List["a_", " ", SuperscriptBox["z_", "c_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List[SqrtBox[FractionBox["1", RowBox[List[RowBox[List["a", " ", SuperscriptBox["z", "c"]]], "+", "1"]]]], " ", SqrtBox[RowBox[List[RowBox[List["a", " ", SuperscriptBox["z", "c"]]], "+", "1"]]]]], "+", RowBox[List[SqrtBox[FractionBox["1", RowBox[List["1", "-", RowBox[List["a", " ", SuperscriptBox["z", "c"]]]]]]], " ", SqrtBox[RowBox[List["1", "-", RowBox[List["a", " ", SuperscriptBox["z", "c"]]]]]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[FractionBox["1", RowBox[List["1", "-", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "c"]]]]]]]]], " ", SqrtBox[RowBox[List[RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", RowBox[List["2", " ", "c"]]]]], "-", "1"]]], " ", RowBox[List["ArcTanh", "[", RowBox[List["a", " ", SuperscriptBox["z", "c"]]], "]"]]]]]]]]]]


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





2003-08-21