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ArcSec




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSec[z] > Representations through equivalent functions > With related functions > Involving sech-1 > Involving sec-1(z2/z2+a1/2) > Involving sec-1(z2/z2+11/2) and sech-1(z2/z2+11/2)





http://functions.wolfram.com/01.18.27.2349.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ArcSec", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]], "]"]], "\[Equal]", RowBox[List[SqrtBox[FractionBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]], SuperscriptBox["z", "2"]]], SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]], SuperscriptBox["z", "2"], SqrtBox[RowBox[List["-", SuperscriptBox["z", RowBox[List["-", "4"]]]]]], RowBox[List["ArcSech", "[", SqrtBox[FractionBox[SuperscriptBox["z", "2"], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]], "]"]]]]]]]]








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> <msqrt> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msqrt> <mfrac> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <msup> <mi> sech </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsec /> <apply> <power /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arcsech /> <apply> <power /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2003-08-21