Euler's formula for Zeta-function: Difference between revisions
(Created page with ": $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} = \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$ == Resources: == *[https://en.wikipedia.org/wiki/Riemann_zeta_function#Euler...") Â |
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'''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 σ > 1 by the sum of the preceding series. | |||
: $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} =Â \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$ | : $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} =Â \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$ | ||
== Resources: == | == Resources: == | ||
Revision as of 16:11, 18 March 2020
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 σ > 1 by the sum of the preceding series.
- $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} = \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$