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http://functions.wolfram.com/07.12.04.0005.01
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Singularities[LegendreQ[\[Nu], \[Mu], 3, z], z] ==
{{1, \[Mu]/2}, {-1, \[Mu]/2}, {ComplexInfinity, -\[Nu] - 1}} /;
Element[\[Nu], Integers] && Element[\[Mu]/2, Integers] && \[Mu]/2 > 0 &&
\[Mu] > -\[Nu] && \[Nu] < -1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "3", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox["\[Mu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", FractionBox["\[Mu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]]]], "}"]]]], "}"]]]], "/;", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Integers"]], "\[And]", RowBox[List[FractionBox["\[Mu]", "2"], "\[Element]", "Integers"]], "\[And]", RowBox[List[FractionBox["\[Mu]", "2"], ">", "0"]], "\[And]", RowBox[List["\[Mu]", ">", RowBox[List["-", "\[Nu]"]]]], "\[And]", RowBox[List["\[Nu]", "<", RowBox[List["-", "1"]]]]]]]]]]
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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> z </mi> </msub> <mo> ( </mo> <mrow> <msubsup> <semantics> <mi> 𝔔 </mi> <annotation encoding='Mathematica'> TagBox["\[GothicCapitalQ]", LegendreQ] </annotation> </semantics> <mi> ν </mi> <mi> μ </mi> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox["z", HoldComplete[LegendreQ, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mi> μ </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mfrac> <mi> μ </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> } </mo> </mrow> <mo> , </mo> <mrow> <mo> { </mo> <mrow> <mover> <mi> ∞ </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> ν </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mfrac> <mi> μ </mi> <mn> 2 </mn> </mfrac> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> <mo> ∧ </mo> <mrow> <mi> μ </mi> <mo> > </mo> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </mrow> <mo> ∧ </mo> <mrow> <mi> ν </mi> <mo> < </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> 𝒮𝒾𝓃ℊ </ci> <ci> z </ci> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> LegendreQ </ci> <ci> 𝔔 </ci> </apply> <ci> ν </ci> </apply> <ci> μ </ci> </apply> <apply> <apply> <ci> HoldComplete </ci> <ci> LegendreQ </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <list> <list> <cn type='integer'> 1 </cn> <apply> <times /> <ci> μ </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <list> <cn type='integer'> -1 </cn> <apply> <times /> <ci> μ </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <list> <apply> <ci> OverTilde </ci> <infinity /> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <cn type='integer'> -1 </cn> </apply> </list> </list> </apply> <apply> <and /> <apply> <in /> <ci> ν </ci> <integers /> </apply> <apply> <in /> <apply> <times /> <ci> μ </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> <apply> <gt /> <ci> μ </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <apply> <lt /> <ci> ν </ci> <cn type='integer'> -1 </cn> </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["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", ",", FractionBox["\[Mu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", FractionBox["\[Mu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["ComplexInfinity", ",", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]]]], "}"]]]], "}"]], "/;", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Integers"]], "&&", RowBox[List[FractionBox["\[Mu]", "2"], "\[Element]", "Integers"]], "&&", RowBox[List[FractionBox["\[Mu]", "2"], ">", "0"]], "&&", RowBox[List["\[Mu]", ">", RowBox[List["-", "\[Nu]"]]]], "&&", RowBox[List["\[Nu]", "<", RowBox[List["-", "1"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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