$x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
$a_1$ |
$1$ |
$0$ |
$4$ |
$0$ |
$48$ |
$0$ |
$640$ |
$0$ |
$8960$ |
$0$ |
$129024$ |
$0$ |
$1892352$ |
$a_2$ |
$1$ |
$1$ |
$11$ |
$40$ |
$235$ |
$1196$ |
$6650$ |
$36632$ |
$205859$ |
$1162732$ |
$6617326$ |
$37840232$ |
$217333390$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$1$ |
$4$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$11$ |
$20$ |
$48$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$40$ |
$104$ |
$256$ |
$640$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$235$ |
$556$ |
$1392$ |
$3520$ |
$8960$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$1196$ |
$3032$ |
$7680$ |
$19584$ |
$50176$ |
$129024$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$6650$ |
$16776$ |
$42848$ |
$109952$ |
$283136$ |
$731136$ |
$1892352$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&0&3&0&6&0&3&0&0\\0&4&0&0&12&0&12&0&24&0\\0&0&10&6&0&3&0&33&0&36\\3&0&6&19&0&27&0&44&0&28\\0&12&0&0&40&0&44&0&84&0\\6&0&3&27&0&46&0&48&0&21\\0&12&0&0&44&0&52&0&96&0\\3&0&33&44&0&48&0&163&0&143\\0&24&0&0&84&0&96&0&184&0\\0&0&36&28&0&21&0&143&0&146\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&4&10&19&40&46&52&163&184&146\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-2$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ |
---|
$-$ | $1$ | $1/2$ | $1/2$ | $0$ | $0$ | $0$ | $0$ |
---|
$a_1=0$ | $1/2$ | $1/2$ | $1/2$ | $0$ | $0$ | $0$ | $0$ |
---|