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 | 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. | ||
: | : <math>\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} = \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}</math> | ||
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== Discussion:== | == Discussion:== | ||
[[Category:Mathematics]] | |||
Latest revision as of 22:21, 30 July 2025
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]