The factorial value of $\pi$ can be found using the gamma function like so: $$\Gamma \left( \pi +1 \right) = \int\limits_0^\infty {s^{\pi} e^{ - s}\,\mathrm{d}s} ≈ 7.1880827$$
This, however, raises the question of if this number is irrational. It is well-known that $\pi$ is irrational, but is $\pi!$ irrational too?