角度分布¶
定义对象 \(x\in\left[-\frac{{\pi}}{{4}},\frac{{\pi}}{{4}}\right]\) 。
\BEGIN{eqnarray *}} f\left(x\right) & = & \sin\left(2x+\frac{{\pi}}{{2}}\right)=\cos\left(2x\right)\\ F\left(x\right) & = & \sin^{{2}}\left(x+\frac{{\pi}}{{4}}\right)\\ G\left(q\right) & = & \arcsin\left(\sqrt{{q}}\right)-\frac{{\pi}}{{4}}\end{{eqnarray* }
\BEGIN{eqnarray *}} \mu & = & 0\\ \mu_{{2}} & = & \frac{{\pi^{{2}}}}{{16}}-\frac{{1}}{{2}}\\ \gamma_{{1}} & = & 0\\ \gamma_{{2}} & = & -2\frac{{\pi^{{4}}-96}}{{\left(\pi^{{2}}-8\right)^{{2}}}}\end{{eqnarray* }
\BEGIN{eqnarray [}} h\left[X\right] & = & 1-\log2\\ & \approx & 0.30685281944005469058\end{{eqnarray] }
\BEGIN{eqnarray *}} M\left(t\right) & = & \int_{{-\frac{{\pi}}{{4}}}}^{{\frac{{\pi}}{{4}}}}\cos\left(2x\right)e^{{xt}}dx\\ & = & \frac{{4\cosh\left(\frac{{\pi t}}{{4}}\right)}}{{t^{{2}}+4}}\end{{eqnarray* }
\[l_{\mathbf{x}}\left(\cdot\right)=-N\overline{\log\left[\cos\left(2\mathbf{x}\right)\right]}\]