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http://functions.wolfram.com/07.09.04.0012.01
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BranchPoints[LegendreP[\[Nu], \[Mu], 3, z], z] == {} /;
Element[\[Nu], Integers] && Element[\[Mu]/2, Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "3", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", "}"]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Integers"]], "]"]], "\[And]", RowBox[List["Element", "[", RowBox[List[FractionBox["\[Mu]", "2"], ",", "Integers"]], "]"]]]]]]]]
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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> ℬ𝒫 </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msubsup> <semantics> <mi> 𝔓 </mi> <annotation encoding='Mathematica'> TagBox["\[GothicCapitalP]", LegendreP] </annotation> </semantics> <mi> ν </mi> <mi> μ </mi> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox["z", HoldComplete[LegendreP, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <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> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> ℬ𝒫 </ci> <ci> z </ci> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> LegendreP </ci> <ci> 𝔓 </ci> </apply> <ci> ν </ci> </apply> <ci> μ </ci> </apply> <apply> <apply> <ci> HoldComplete </ci> <ci> LegendreP </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <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> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["LegendreP", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "3", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", "}"]], "/;", RowBox[List[RowBox[List["\[Nu]", "\[Element]", "Integers"]], "&&", RowBox[List[FractionBox["\[Mu]", "2"], "\[Element]", "Integers"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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LegendreP[n,z] | LegendreP[nu,z] | LegendreP[nu,mu,z] | LegendreP[n,mu,2,z] | LegendreP[nu,mu,2,z] | |
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