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ArcSec




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSec[z] > Representations through equivalent functions > With related functions > Involving tan-1 > Involving sec-1(1+z/1-z) > Involving sec-1(1+z/1-z) and tan-1(1/z1/2)





http://functions.wolfram.com/01.18.27.0463.01









  


  








Input Form





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








Standard Form





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








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










Rule Form





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


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





2003-08-21