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http://functions.wolfram.com/07.10.20.0004.01
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D[LegendreQ[\[Nu], z], {z, 2}] ==
(\[Nu] (2 z LegendreQ[\[Nu] - 1, z] + (z^2 (\[Nu] - 1) - \[Nu] - 1)
LegendreQ[\[Nu], z]))/(z^2 - 1)^2
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", FractionBox[RowBox[List["\[Nu]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "z", " ", RowBox[List["LegendreQ", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "1"]], ")"]]]], "-", "\[Nu]", "-", "1"]], ")"]], " ", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "2"]]]]]]
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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> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mn> 2 </mn> </msup> <mrow> <msub> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox["Q", LegendreQ] </annotation> </semantics> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mi> ν </mi> <mtext> </mtext> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox["Q", LegendreQ] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox["Q", LegendreQ] </annotation> </semantics> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> LegendreQ </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <ci> ν </ci> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <ci> LegendreQ </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> LegendreQ </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[Nu]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "z", " ", RowBox[List["LegendreQ", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "1"]], ")"]]]], "-", "\[Nu]", "-", "1"]], ")"]], " ", RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], ")"]], "2"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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