Difference between revisions of "Fibonacci polynomial"
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m (Tom moved page Fibonacci polynomial to Fibonacci) |
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xF_{n-1}(x)+F_{n-2}(x)&; n\geq 2. | xF_{n-1}(x)+F_{n-2}(x)&; n\geq 2. | ||
\end{array} \right.$$ | \end{array} \right.$$ | ||
| + | |||
| + | The first few Fibonacci polynomials are | ||
| + | $$F_0(x)=1,$$ | ||
| + | $$F_1(x)=1,$$ | ||
| + | $$F_2(x)=x,$$ | ||
| + | $$F_3(x)=x^2+1,$$ | ||
| + | $$F_4(x)=x^3+2x,$$ | ||
| + | $$F_5(x)=x^4+3x^2+1.$$ | ||
| + | |||
Note the similarity with the [[Lucas polynomial|Lucas polynomials]]. | Note the similarity with the [[Lucas polynomial|Lucas polynomials]]. | ||
Revision as of 22:55, 11 April 2015
Fibonacci polynomials are defined by $$F_n(x)=\left\{ \begin{array}{ll} 0&; n=0 \\ 1&; n=1 \\ xF_{n-1}(x)+F_{n-2}(x)&; n\geq 2. \end{array} \right.$$
The first few Fibonacci polynomials are $$F_0(x)=1,$$ $$F_1(x)=1,$$ $$F_2(x)=x,$$ $$F_3(x)=x^2+1,$$ $$F_4(x)=x^3+2x,$$ $$F_5(x)=x^4+3x^2+1.$$
Note the similarity with the Lucas polynomials.
