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\begin{document}



\begin{center}

%%\textbf{Formulas}

Useful identities:
\begin{gather*}
  \cos \theta = \frac{e^{i\theta}+e^{-i\theta}}{2} \\
  \sin \theta = \frac{e^{i\theta}-e^{-i\theta}}{2i} \\
  \cos^2 \theta = \tfrac12 \, (1 + \cos 2\theta) \\
  \sin^2 \theta = \tfrac12 \, (1 - \cos 2\theta) \\
  f_k = \frac1{\sqrt{L}} \int_{a}^{a+L} \e^{-\frac{2\pi i k x}L} \, f(x)
  \, dx \\
  f(x) = \frac1{\sqrt{L}} \sum_{k=-\infty}^\infty f_k \,
         \e^{\frac{2\pi i k x}L} \\
  \tilde f(\xi)
  = \frac1{\sqrt{2\pi}} \int_{-\infty}^\infty e^{-i\xi x} \, f(x) \,
  dx \\
  f(x)
  = \frac1{\sqrt{2\pi}} \int_{-\infty}^\infty e^{i\xi x} \,
  \tilde f(\xi) \, d\xi \\
  \delta(x)
  = \frac1{2\pi} \int_{-\infty}^\infty e^{i\xi x} \, d\xi \\
  (f * g)(x) = \int_{-\infty}^\infty f(y) \, g(x - y) \, \mathrm{d} y \\
  f(v) = \frac1{\sqrt{2\pi} \sigma} \, \mathrm{e}^{-\tfrac{(v-\mu)^2}{2
      \sigma^2}}  \\
  P(A \cap B)=P(A) P(B|A) \\
  P(A)= P(B) P(A|B)+ P(\overline{B}) P(A|\overline{B})
\end{gather*}


\end{center}

\end{document}
