Difference between revisions of "Dickson polynomial"
From specialfunctionswiki
(Created page with "The Dickson polynomials of the first kind are $$\left\{ \begin{array}{ll} D_0(x,\alpha) &=2 \\ D_n(x,\alpha) &=\displaystyle\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor} \dfrac{n}{...") |
|||
| Line 10: | Line 10: | ||
E_n(x,\alpha) &= \displaystyle\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor} {{n-k} \choose k} (-\alpha)^k x^{n-2k}. | E_n(x,\alpha) &= \displaystyle\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor} {{n-k} \choose k} (-\alpha)^k x^{n-2k}. | ||
\end{array} \right.$$ | \end{array} \right.$$ | ||
| + | |||
| + | {{:Orthogonal polynomials footer}} | ||
Revision as of 21:55, 22 March 2015
The Dickson polynomials of the first kind are $$\left\{ \begin{array}{ll} D_0(x,\alpha) &=2 \\ D_n(x,\alpha) &=\displaystyle\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor} \dfrac{n}{n-k} {{n-p} \choose p} (-\alpha)^p x^{n-2k}. \end{array} \right.$$
The Dickson polynomials of the second kind are $$\left\{ \begin{array}{ll} E_0(x,\alpha) &= 1 \\ E_n(x,\alpha) &= \displaystyle\sum_{k=0}^{\lfloor \frac{n}{2} \rfloor} {{n-k} \choose k} (-\alpha)^k x^{n-2k}. \end{array} \right.$$
