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Sec




Mathematica Notation

Traditional Notation









Elementary Functions > Sec[z] > Representations through equivalent functions > With related functions > Involving csc





http://functions.wolfram.com/01.11.27.0033.01









  


  








Input Form





Sec[z] - I Csc[z] == -2 I E^(I z) Csc[2 z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sec", "[", "z", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Csc", "[", "z", "]"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "z"]]], " ", RowBox[List["Csc", "[", RowBox[List["2", " ", "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> <mrow> <mi> sec </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <sec /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <csc /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <apply> <csc /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Sec", "[", "z_", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Csc", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "z"]]], " ", RowBox[List["Csc", "[", RowBox[List["2", " ", "z"]], "]"]]]]]]]]


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





2001-10-29