$e=mc^2$ E_1= \(m c^3\)
and now, the end is near and so I face the final $$\LaTeX$$
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1. monospace:
1. let's take this Poisson integral :
let define $J = \int\limits_{-\infty}^{\infty}e^{-x^2}dx$ now use substitution $x=r\cdot cos(ϕ)$, $y=r\cdot sin(ϕ)$, so $x^2+y^2=r^2$, and find $J^2 = \int\limits_{-\infty}^{\infty}e^{-x^2}dx\int\limits_{-\infty}^{\infty}e^{y^2}dy = \{dxdy = rdrd\phi\} = \int\limits_{0}^{\infty}\int\limits_{0}^{2\pi}e^{-r^2}rdrd\phi$ so $J^2 = 2\pi(-\frac12)\int\limits_{0}^{\infty}e^{-r^2}d(r^2)$ = $-\pi e^{-r^2}\vert_0^{\infty} = \pi$ we can find that $J = \sqrt{\pi}$ after substitue $x \rightarrow x/\sqrt 2$
so we have $\int\limits_{-\infty}^{\infty}e^{-\frac{x^2}{2}}\frac{dx}{\sqrt{2}} \rightarrow \int\limits_{-\infty}^{\infty}e^{-\frac{x^2}{2}}dx = \sqrt{2\pi}$ now make following assumptions :
$\mu \ge 0$ and $\sigma \ge 0$