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variants of this functions
ChebyshevT




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevT[nu,z] > General characteristics > Poles and essential singularities > With respect to z





http://functions.wolfram.com/07.04.04.0006.01









  


  








Input Form





Singularities[ChebyshevT[\[Nu], z], z] == {{ComplexInfinity, Abs[\[Nu]]}} /; Element[\[Nu], Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], "}"]], "}"]]]], "/;", RowBox[List["\[Nu]", "\[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> <msub> <mi> &#119982;&#119998;&#120003;&#8458; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msub> <mi> T </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> &#957; </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#957; </mi> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#119982;&#119998;&#120003;&#8458; </ci> <ci> z </ci> </apply> <apply> <ci> ChebyshevT </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> <list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <apply> <abs /> <ci> &#957; </ci> </apply> </list> </list> </apply> <apply> <in /> <ci> &#957; </ci> <ci> &#8484; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], "}"]], "}"]], "/;", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]


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





2001-10-29