$x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
$a_1$ |
$1$ |
$0$ |
$2$ |
$0$ |
$16$ |
$0$ |
$160$ |
$0$ |
$1792$ |
$0$ |
$21504$ |
$0$ |
$270336$ |
$a_2$ |
$1$ |
$2$ |
$6$ |
$20$ |
$78$ |
$332$ |
$1516$ |
$7240$ |
$35734$ |
$180620$ |
$929940$ |
$4858328$ |
$25687052$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$2$ |
$2$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$6$ |
$8$ |
$16$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$20$ |
$34$ |
$72$ |
$160$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$78$ |
$152$ |
$336$ |
$768$ |
$1792$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$332$ |
$708$ |
$1616$ |
$3776$ |
$8960$ |
$21504$ |
$\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$1516$ |
$3408$ |
$7968$ |
$18944$ |
$45568$ |
$110592$ |
$270336$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&1&0&0&2&0&1&0&2\\0&2&0&0&4&0&2&0&6&0\\1&0&3&2&0&4&0&5&0&6\\0&0&2&6&0&4&0&10&0&6\\0&4&0&0&10&0&8&0&16&0\\2&0&4&4&0&8&0&10&0&10\\0&2&0&0&8&0&10&0&14&0\\1&0&5&10&0&10&0&25&0&16\\0&6&0&0&16&0&14&0&28&0\\2&0&6&6&0&10&0&16&0&16\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&2&3&6&10&8&10&25&28&16\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-2$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ |
---|
$-$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
---|
$a_1=0$ | $1/2$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
---|