Uploaded November 2021 | Updated September 2026, 1 week ago

---

In this video, I will talk about a function with a very interesting property: Even though the function itself is nonzero, all its derivatives at 0 are zero! In particular, the Maclaurin series of this function is identically 0. This is what is called a non analytic smooth function, and is very important in analysis and beyond.

YouTube channel: youtube.com/drpeyam
TikTok: tiktok.com/@drpeyam
Instagram: instagram.com/peyamstagram
Twitter: twitter.com/drpeyam
Teespring merch: teespring.com/stores/dr-peyam