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ArcSec




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSec[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations > Involving sec-1(2 z/z+a1/2) > Involving sec-1(2z/z+11/2) and sec-1(z)





http://functions.wolfram.com/01.18.16.0065.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["ArcSec", "[", SqrtBox[FractionBox[RowBox[List["2", " ", "z"]], RowBox[List["z", "+", "1"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "-", RowBox[List[FractionBox[RowBox[List[SqrtBox["z"], SqrtBox[RowBox[List["z", "+", "1"]]]]], "2"], " ", SqrtBox[FractionBox["1", "z"]], " ", SqrtBox[FractionBox["1", RowBox[List["z", "+", "1"]]]], RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["ArcSec", "[", "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> <msqrt> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mfrac> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <msqrt> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mn> 1 </mn> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> - </mo> <mrow> <msup> <mi> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsec /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arcsec /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


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





2003-08-21