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Csc




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.10.19.0012.01









  


  








Input Form





Conjugate[Csc[z]] == 1/(Cosh[Im[z]] Sin[Re[z]] - I Cos[Re[z]] Sinh[Im[z]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["Csc", "[", "z", "]"]], "]"]], "\[Equal]", FractionBox["1", RowBox[List[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["Re", "[", "z", "]"]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cos", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]]]]]]]]]








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> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> <mo> &#10869; </mo> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> OverBar </ci> <apply> <csc /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <cosh /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <apply> <sin /> <apply> <real /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <cos /> <apply> <real /> <ci> z </ci> </apply> </apply> <apply> <sinh /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> </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["Csc", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox["1", RowBox[List[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["Re", "[", "z", "]"]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cos", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]]]]]]]]]


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





2007-05-02