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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Polynomials > LegendreP[n,mu,2,z] > General characteristics > Poles and essential singularities > With respect to z





http://functions.wolfram.com/05.07.04.0004.01









  


  








Input Form





Singularities[LegendreP[n, \[Mu], 2, z], z] == {{ComplexInfinity, n}} /; Element[\[Mu]/2, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["n", ",", "\[Mu]", ",", "2", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "n"]], "}"]], "}"]]]], "/;", RowBox[List[FractionBox["\[Mu]", "2"], "\[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> <msubsup> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mi> n </mi> <mi> &#956; </mi> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, HoldComplete[LegendreP, 2]] </annotation> </semantics> <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> <mi> n </mi> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mfrac> <mi> &#956; </mi> <mn> 2 </mn> </mfrac> <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> LegendreP </ci> <ci> n </ci> <ci> &#956; </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <ci> n </ci> </list> </list> </apply> <apply> <in /> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <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["LegendreP", "[", RowBox[List["n_", ",", "\[Mu]_", ",", "2", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "n"]], "}"]], "}"]], "/;", RowBox[List[FractionBox["\[Mu]", "2"], "\[Element]", "Integers"]]]]]]]]


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





2001-10-29