Formula Catalog

$\mathcal{L} = -\sum_{t=1}^{T}\sum_{-m\le j\le m, j\ne 0}\log P(w_{t+j}|w_t)$

$\vec{F} = m \vec{a}$

$r = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}}$

$i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t)=\hat{H}\Psi(\mathbf{r},t)$

$a^2 + b^2 = c^2$

$\sin^{2}x + \cos^{2}x = 1$

$e^{i\pi} + 1 = 0$

$x_{n+1} = r x_n (1 - x_n)$

$P(X = k) = p^{k} (1-p)^{1-k}$