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http://functions.wolfram.com/07.37.04.0017.01
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Singularities[SphericalHarmonicY[\[Lambda], \[Mu], \[CurlyTheta],
\[CurlyPhi]], \[CurlyTheta]] == {{ComplexInfinity, -\[Lambda] - 1}} /;
Element[\[Mu]/2, Integers] && Element[-\[Lambda], Integers] && -\[Lambda] > 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["SphericalHarmonicY", "[", RowBox[List["\[Lambda]", ",", "\[Mu]", ",", "\[CurlyTheta]", ",", "\[CurlyPhi]"]], "]"]], ",", "\[CurlyTheta]"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", RowBox[List[RowBox[List["-", "\[Lambda]"]], "-", "1"]]]], "}"]], "}"]]]], "/;", RowBox[List[RowBox[List[FractionBox["\[Mu]", "2"], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "\[Lambda]"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["-", "\[Lambda]"]], ">", "0"]]]]]]]]
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<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> 𝒮𝒾𝓃ℊ </mi> <mi> ϑ </mi> </msub> <mo> ( </mo> <mrow> <msubsup> <mi> Y </mi> <mi> λ </mi> <mi> μ </mi> </msubsup> <mo> ( </mo> <mrow> <mi> ϑ </mi> <mo> , </mo> <mi> φ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> λ </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> } </mo> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mfrac> <mi> μ </mi> <mn> 2 </mn> </mfrac> <mo> ∈ </mo> <mi> ℤ </mi> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mo> - </mo> <mi> λ </mi> </mrow> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> 𝒮𝒾𝓃ℊ </ci> <ci> ϑ </ci> </apply> <apply> <ci> SphericalHarmonicY </ci> <ci> λ </ci> <ci> μ </ci> <ci> ϑ </ci> <ci> φ </ci> </apply> </apply> <list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> λ </ci> </apply> <cn type='integer'> -1 </cn> </apply> </list> </list> </apply> <apply> <and /> <apply> <in /> <apply> <times /> <ci> μ </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> ℤ </ci> </apply> <apply> <in /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> λ </ci> </apply> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[RowBox[List["SphericalHarmonicY", "[", RowBox[List["\[Lambda]_", ",", "\[Mu]_", ",", "\[CurlyTheta]_", ",", "\[CurlyPhi]_"]], "]"]], ",", "\[CurlyTheta]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", RowBox[List[RowBox[List["-", "\[Lambda]"]], "-", "1"]]]], "}"]], "}"]], "/;", RowBox[List[RowBox[List[FractionBox["\[Mu]", "2"], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "\[Lambda]"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "\[Lambda]"]], ">", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
