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http://functions.wolfram.com/07.37.04.0021.01
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BranchPoints[SphericalHarmonicY[\[Lambda], \[Mu], \[CurlyTheta],
\[CurlyPhi]], \[Mu]] == {SequenceList[\[Lambda] + n,
Element[n, Integers] && n > 0], SequenceList[-\[Lambda] - n,
Element[n, Integers] && n > 0], ComplexInfinity}
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Cell[BoxData[RowBox[List[RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["SphericalHarmonicY", "[", RowBox[List["\[Lambda]", ",", "\[Mu]", ",", "\[CurlyTheta]", ",", "\[CurlyPhi]"]], "]"]], ",", "\[Mu]"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["\[Lambda]", "+", "n"]], ",", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]], "]"]], ",", RowBox[List["SequenceList", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[Lambda]"]], "-", "n"]], ",", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]], "]"]], ",", "ComplexInfinity"]], "}"]]]]]]
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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> <msub> <mi> ℬ𝒫 </mi> <mi> μ </mi> </msub> <mo> ( </mo> <semantics> <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> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox["Y", "\[Lambda]", "\[Mu]"], "(", RowBox[List["\[CurlyTheta]", ",", "\[CurlyPhi]"]], ")"]], InterpretTemplate[Function[List[$CellContext`a, $CellContext`b], Zeta[$CellContext`a, $CellContext`b]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mi> λ </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> λ </mi> </mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <mi> ℬ𝒫 </mi> <mi> μ </mi> </msub> <mo> ( </mo> <semantics> <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> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox["Y", "\[Lambda]", "\[Mu]"], "(", RowBox[List["\[CurlyTheta]", ",", "\[CurlyPhi]"]], ")"]], InterpretTemplate[Function[List[$CellContext`a, $CellContext`b], Zeta[$CellContext`a, $CellContext`b]]]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <mi> λ </mi> <mo> + </mo> <mi> n </mi> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> λ </mi> </mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> </mrow> <mo> } </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["SphericalHarmonicY", "[", RowBox[List["\[Lambda]_", ",", "\[Mu]_", ",", "\[CurlyTheta]_", ",", "\[CurlyPhi]_"]], "]"]], ",", "\[Mu]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["SequenceList", "[", RowBox[List[RowBox[List["\[Lambda]", "+", "n"]], ",", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]], "]"]], ",", RowBox[List["SequenceList", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[Lambda]"]], "-", "n"]], ",", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]], "]"]], ",", "ComplexInfinity"]], "}"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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