Euler's formula for Zeta-function

Leonhard Euler (b. 1707)

Euler's formula for Zeta-function 1740

The Riemann zeta function is defined as the analytic continuation of the function defined for [math]\displaystyle{ \sigma \gt 1 }[/math] by the sum of the preceding series.

[math]\displaystyle{ \sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} = \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}} }[/math]

Resources:

• Euler's formula for Zeta-function