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Csc




Mathematica Notation

Traditional Notation









Elementary Functions > Csc[z] > General characteristics > Poles and essential singularities





http://functions.wolfram.com/01.10.04.0007.01









  


  








Input Form





Residue[Csc[z], {z, Pi k}] == (-1)^k /; Element[k, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Residue", "[", RowBox[List[RowBox[List["Csc", "[", "z", "]"]], ",", RowBox[List["{", RowBox[List["z", ",", RowBox[List["\[Pi]", " ", "k"]]]], "}"]]]], "]"]], "\[Equal]", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"]]], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]








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> <mrow> <msub> <mi> res </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> csc </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> res </ci> <ci> z </ci> </apply> <apply> <csc /> <ci> z </ci> </apply> </apply> <apply> <times /> <pi /> <ci> k </ci> </apply> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Residue", "[", RowBox[List[RowBox[List["Csc", "[", "z_", "]"]], ",", RowBox[List["{", RowBox[List["z_", ",", RowBox[List["\[Pi]", " ", "k_"]]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]


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





2001-10-29