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LucasL




Mathematica Notation

Traditional Notation









Integer Functions > LucasL[nu] > Generating functions





http://functions.wolfram.com/04.22.11.0001.01









  


  








Input Form





LucasL[n] == SeriesTerm[(2 - t)/(1 - t - t^2), {t, 0, n}] /; Element[n, Integers] && n >= 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LucasL", "[", "n", "]"]], "\[Equal]", RowBox[List["SeriesTerm", "[", RowBox[List[FractionBox[RowBox[List["2", "-", "t"]], RowBox[List["1", "-", "t", "-", SuperscriptBox["t", "2"]]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "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> n </mi> </msub> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <msup> <mi> t </mi> <mi> n </mi> </msup> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> t </mi> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> t </mi> <mo> - </mo> <msup> <mi> t </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox[&quot;L&quot;, LucasL] </annotation> </semantics> <mi> n </mi> </msub> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> [ </mo> <msup> <mi> t </mi> <mi> n </mi> </msup> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> t </mi> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> t </mi> <mo> - </mo> <msup> <mi> t </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LucasL", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["SeriesTerm", "[", RowBox[List[FractionBox[RowBox[List["2", "-", "t"]], RowBox[List["1", "-", "t", "-", SuperscriptBox["t", "2"]]]], ",", RowBox[List["{", RowBox[List["t", ",", "0", ",", "n"]], "}"]]]], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]


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





2007-05-02