Mathematics - My Favorite Euler Formulas 🔗

Euler’s formula in complex analysis 🔗

`e^(ix) = cos x + i sin x`

See wikipedia.

Euler’s identity 🔗

`e^(ipi) + 1 = 0`

See wikipedia.

Euler’s number 🔗

`e = sum_(n = 0)^infty 1/(n!) = 1/1 + 1/1 + 1/(1 * 2) + 1/(1 * 2 * 3) + cdots`

See wikipedia.

Euler’s product formula for the Riemann zeta function 🔗

`zeta(s) = sum_(n=1)^infty 1/(n^s) = prod_(p bbb " prime") 1/(1 - p^-s)`

See wikipedia.

See also Riemann hypothesis, one of the Millennium Prize Problems: wikipedia.