![rac{1}{arepsilon}{athrm{Im}}eft[ f(x+iarepsilon) ight] = f’(x) + athcal{O}(arepsilon^2)](https://lemmy.world/pictrs/image/a276b227-6e75-41a3-8c20-072ad1ca1846.png){kind=link}
This is the first one that’s new to me! Really interesting, I guess the big problem is that you need to actually be able to evaluate the analytic extension.
Comment on What are the most mindblowing fact in mathematics?
AlmightySnoo@lemmy.world 10 months ago
The fact that complex numbers give you a better approximation of the derivative than classical finite difference at almost no extra cost:
rac{1}{arepsilon}{athrm{Im}}eft[ f(x+iarepsilon) ight] = f’(x) + athcal{O}(arepsilon^2)
Higher-order derivatives can also be obtained using hypercomplex numbers.
MBM@lemmings.world 10 months ago
efrique@lemm.ee 10 months ago
Well, that’s something I hadn’t seen before.