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http://functions.wolfram.com/04.22.20.0002.01
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D[LucasL[\[Nu]], {\[Nu], 2}] == (-GoldenRatio^(-\[Nu])) Pi^2 Cos[Pi \[Nu]] +
GoldenRatio^\[Nu] Log[GoldenRatio]^2 + (Cos[Pi \[Nu]] Log[GoldenRatio]^2)/
GoldenRatio^\[Nu] + (2 Pi Log[GoldenRatio] Sin[Pi \[Nu]])/GoldenRatio^\[Nu]
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["\[Nu]", ",", "2"]], "}"]]], RowBox[List["LucasL", "[", "\[Nu]", "]"]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["GoldenRatio", RowBox[List["-", "\[Nu]"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], "+", RowBox[List[SuperscriptBox["GoldenRatio", "\[Nu]"], " ", SuperscriptBox[RowBox[List["Log", "[", "GoldenRatio", "]"]], "2"]]], "+", RowBox[List[SuperscriptBox["GoldenRatio", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", SuperscriptBox[RowBox[List["Log", "[", "GoldenRatio", "]"]], "2"]]], "+", RowBox[List["2", " ", SuperscriptBox["GoldenRatio", RowBox[List["-", "\[Nu]"]]], " ", "\[Pi]", " ", RowBox[List["Log", "[", "GoldenRatio", "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]]]]]]]]
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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> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> ν </mi> </msub> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> ν </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo>  </mo> <mrow> <mrow> <msup> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mi> ν </mi> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> ν </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> LucasL </ci> <ci> ν </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> GoldenRatio </ci> <ci> ν </ci> </apply> <apply> <power /> <apply> <ln /> <ci> GoldenRatio </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> GoldenRatio </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> <apply> <power /> <apply> <ln /> <ci> GoldenRatio </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> GoldenRatio </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <pi /> <apply> <sin /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> <apply> <ln /> <ci> GoldenRatio </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> GoldenRatio </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <cos /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </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["\[Nu]_", ",", "2"]], "}"]]]]], RowBox[List["LucasL", "[", "\[Nu]_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["GoldenRatio", RowBox[List["-", "\[Nu]"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], "+", RowBox[List[SuperscriptBox["GoldenRatio", "\[Nu]"], " ", SuperscriptBox[RowBox[List["Log", "[", "GoldenRatio", "]"]], "2"]]], "+", RowBox[List[SuperscriptBox["GoldenRatio", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", SuperscriptBox[RowBox[List["Log", "[", "GoldenRatio", "]"]], "2"]]], "+", RowBox[List["2", " ", SuperscriptBox["GoldenRatio", RowBox[List["-", "\[Nu]"]]], " ", "\[Pi]", " ", RowBox[List["Log", "[", "GoldenRatio", "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
