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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(z2-1/z2+1) > Involving sec-1(z2-1/z2+1) and tanh-1(1/z)





http://functions.wolfram.com/01.18.27.1591.01









  


  










Input Form





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










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mtext> </mtext> <mrow> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mrow> <msqrt> <mfrac> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> <mo> - </mo> <mtext> </mtext> <mrow> <msqrt> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </msqrt> <mo> &#8290; 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Rule Form





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










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





2003-08-21