4 ms·

I wouldn't say power series are the 'reason' they are related. The more intuitive reason for Euler's identity is the combination of e^x being its own derivative

I wouldn't say power series are the 'reason' they are related. The more intuitive reason for Euler's identity is the combination of e^x being its own derivative, and the relationship between complex multiplication and rotation.

roenxi 5y ago
"its own derivative" is defined in terms of things happening at infinity though. Calculus is very much a study of what happens to things at the infinite and infinitesimal; and e has its heft because of calculus.
- eutectic 5y ago
  OK, agreed.