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Euler's formula for Zeta-function: Difference between revisions

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'''''Euler's formula for Zeta-function''''' 1740
'''''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.
The Riemann zeta function is defined as the analytic continuation of the function defined for <math>\sigma > 1</math> by the sum of the preceding series.


: $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} =  \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$
: <math>\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} =  \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}</math>