$x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
$a_1$ |
$1$ |
$0$ |
$4$ |
$0$ |
$48$ |
$0$ |
$640$ |
$0$ |
$8960$ |
$0$ |
$129024$ |
$0$ |
$1892352$ |
$a_2$ |
$1$ |
$2$ |
$10$ |
$44$ |
$230$ |
$1212$ |
$6628$ |
$36696$ |
$205766$ |
$1162988$ |
$6616940$ |
$37841256$ |
$217331804$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$2$ |
$4$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$10$ |
$20$ |
$48$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$44$ |
$104$ |
$256$ |
$640$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$230$ |
$556$ |
$1392$ |
$3520$ |
$8960$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$1212$ |
$3032$ |
$7680$ |
$19584$ |
$50176$ |
$129024$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$6628$ |
$16776$ |
$42848$ |
$109952$ |
$283136$ |
$731136$ |
$1892352$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&1&2&0&4&0&5&0&4\\0&4&0&0&12&0&12&0&24&0\\1&0&7&8&0&10&0&27&0&24\\2&0&8&18&0&22&0&48&0&36\\0&12&0&0&40&0&44&0&84&0\\4&0&10&22&0&32&0&60&0&46\\0&12&0&0&44&0&52&0&96&0\\5&0&27&48&0&60&0&153&0&122\\0&24&0&0&84&0&96&0&184&0\\4&0&24&36&0&46&0&122&0&104\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&4&7&18&40&32&52&153&184&104\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-2$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ |
---|
$-$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
---|
$a_1=0$ | $1/2$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
---|