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Csch




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.23.04.0006.01









  


  








Input Form





Singularities[Csch[z], z] == {SequenceList[{Pi I k, 1}, Element[k, Integers]], {ComplexInfinity, Infinity}}








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["Csch", "[", "z", "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "k"]], ",", "1"]], "}"]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "}"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> } </mo> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#119982;&#119998;&#120003;&#8458; </ci> <ci> z </ci> </apply> <apply> <csch /> <ci> z </ci> </apply> </apply> <list> <list> <apply> <ci> Condition </ci> <list> <apply> <times /> <pi /> <imaginaryi /> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </list> <apply> <in /> <ci> k </ci> <ci> &#8484; </ci> </apply> </apply> </list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <infinity /> </list> </list> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["Csch", "[", "z_", "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "k"]], ",", "1"]], "}"]], ",", RowBox[List["k", "\[Element]", "Integers"]]]], "]"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "}"]]]]]]


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





2001-10-29