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Sec




Mathematica Notation

Traditional Notation









Elementary Functions > Sec[z] > Complex characteristics > Conjugate value





http://functions.wolfram.com/01.11.19.0006.01









  


  








Input Form





Conjugate[Sec[x + I y]] == 1/(Cos[x] Cosh[y] + I Sin[x] Sinh[y])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["Sec", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "]"]], "\[Equal]", FractionBox["1", RowBox[List[RowBox[List[RowBox[List["Cos", "[", "x", "]"]], " ", RowBox[List["Cosh", "[", "y", "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sin", "[", "x", "]"]], " ", RowBox[List["Sinh", "[", "y", "]"]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mover> <mrow> <mi> sec </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> y </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> OverBar </ci> <apply> <sec /> <apply> <plus /> <ci> x </ci> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <cos /> <ci> x </ci> </apply> <apply> <cosh /> <ci> y </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <sin /> <ci> x </ci> </apply> <apply> <sinh /> <ci> y </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Conjugate", "[", RowBox[List["Sec", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List[RowBox[List[RowBox[List["Cos", "[", "x", "]"]], " ", RowBox[List["Cosh", "[", "y", "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Sin", "[", "x", "]"]], " ", RowBox[List["Sinh", "[", "y", "]"]]]]]]]]]]]


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





2001-10-29