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ArcSec




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.18.27.0273.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ArcSec", "[", FractionBox["1", RowBox[List["1", "-", RowBox[List["2", " ", SuperscriptBox["z", "2"]]]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", SqrtBox[SuperscriptBox["z", "2"]]]], "z"], "-", RowBox[List["2", FractionBox[SqrtBox[SuperscriptBox["z", "2"]], "z"], RowBox[List["ArcCos", "[", "z", "]"]]]]]]]]]]








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> <mn> 1 </mn> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> </mrow> <mi> z </mi> </mfrac> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msqrt> <mtext> </mtext> </mrow> <mi> z </mi> </mfrac> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsec /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <arccos /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2003-08-21