I just uploaded an article that I recently wrote, dealing with a semi-rigorous proof of the solution of Gaussian integrals in the complex, i.e.
\[ \int_{-\infty}^{\infty}{\mathrm{d}x \, \mathrm{e}^{-a x^2 + bx} = \mathrm{e}^{b^2/(4a)} \sqrt{\frac{\pi}{a}}}, \quad a, b \in \mathbb{C}, \quad \text{Re}(a) \geq 0,\]
where \(\text{Re}(a) = 0 \implies \text{Im}(a) \neq 0 \, \wedge \, \text{Re}(b) = 0\).
You can find it under the menu item “Teaching“.
See you there!
