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GoldenRatio




Mathematica Notation

Traditional Notation









Constants > GoldenRatio > Identities > Functional identities





http://functions.wolfram.com/02.02.17.0008.01









  


  








Input Form





GoldenRatio^n == GoldenRatio^(n - 1) + GoldenRatio^(n - 2) /; Element[n, Integers] && n > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["GoldenRatio", "n"], "\[Equal]", RowBox[List[SuperscriptBox["GoldenRatio", RowBox[List["n", "-", "1"]]], "+", SuperscriptBox["GoldenRatio", RowBox[List["n", "-", "2"]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "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> <msup> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> <mi> n </mi> </msup> <mo> &#10869; </mo> <mrow> <msup> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> + </mo> <msup> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> <mrow> <mi> n </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <msup> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[List[], Integers]] </annotation> </semantics> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <ci> GoldenRatio </ci> <ci> n </ci> </apply> <apply> <plus /> <apply> <power /> <ci> GoldenRatio </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> GoldenRatio </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["GoldenRatio", "n_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["GoldenRatio", RowBox[List["n", "-", "1"]]], "+", SuperscriptBox["GoldenRatio", RowBox[List["n", "-", "2"]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]


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





2007-05-02