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LucasL




Mathematica Notation

Traditional Notation









Integer Functions > LucasL[nu] > Series representations > Generalized power series > Expansions at nu==0





http://functions.wolfram.com/04.22.06.0005.01









  


  








Input Form





LucasL[\[Nu]] \[Proportional] 2 + (-(Pi^2/2) + Log[GoldenRatio]^2) \[Nu]^2 + ((Pi^2 Log[GoldenRatio])/2) \[Nu]^3 + \[Ellipsis] /; (\[Nu] -> 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LucasL", "[", "\[Nu]", "]"]], "\[Proportional]", RowBox[List["2", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "2"], "2"]]], "+", SuperscriptBox[RowBox[List["Log", "[", "GoldenRatio", "]"]], "2"]]], ")"]], SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["Log", "[", "GoldenRatio", "]"]]]], "2"], " ", SuperscriptBox["\[Nu]", "3"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List["(", RowBox[List["\[Nu]", "\[Rule]", "0"]], ")"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox[&quot;L&quot;, LucasL] </annotation> </semantics> <mi> &#957; </mi> </msub> <mo> &#8733; </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> - </mo> <mfrac> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <msup> <mi> &#960; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#957; </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> LucasL </ci> <ci> &#957; </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ln /> <ci> GoldenRatio </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ln /> <ci> GoldenRatio </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <ci> Rule </ci> <ci> &#957; </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LucasL", "[", "\[Nu]_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[Pi]", "2"], "2"]]], "+", SuperscriptBox[RowBox[List["Log", "[", "GoldenRatio", "]"]], "2"]]], ")"]], " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["Log", "[", "GoldenRatio", "]"]]]], ")"]], " ", SuperscriptBox["\[Nu]", "3"]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List["\[Nu]", "\[Rule]", "0"]], ")"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2007-05-02