Math

Convolution

\begin{align} \frac{d}{dt} \int_0^t f(\tau)g(t-\tau) d \tau = \int_0^t f(\tau)\frac{d}{dt}g(t-\tau) d \tau + f(t)g(0) \nonumber \end{align}

Nemes approximation

\begin{align} \Gamma(x) \approx \sqrt{\frac{2 \pi}{x}} \times \left( \frac{1}{e} \left(x + \frac{1}{12x-\frac{1}{10x}} \right) \right)^x \nonumber \end{align} Nemes, Gergő. "New asymptotic expansion for the Gamma function." Archiv der Mathematik 95, no. 2 (2010): 161-169.