Difference between revisions of "Derivative of prime zeta"
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(Created page with "==Theorem== The following formula holds: $$P'(z)=-\displaystyle\sum_{p \mathrm{\hspace{2pt} prime}} \dfrac{\log(p)}{p^z},$$ where $P$ denotes the prime zeta function and $...") |
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The following formula holds: | The following formula holds: | ||
$$P'(z)=-\displaystyle\sum_{p \mathrm{\hspace{2pt} prime}} \dfrac{\log(p)}{p^z},$$ | $$P'(z)=-\displaystyle\sum_{p \mathrm{\hspace{2pt} prime}} \dfrac{\log(p)}{p^z},$$ | ||
| − | where $P$ denotes the [[prime zeta]] function and $\log$ denotes the [[logarithm]]. | + | where $P$ denotes the [[prime zeta P|prime zeta]] function and $\log$ denotes the [[logarithm]]. |
==Proof== | ==Proof== | ||
Revision as of 18:43, 20 September 2016
Theorem
The following formula holds: $$P'(z)=-\displaystyle\sum_{p \mathrm{\hspace{2pt} prime}} \dfrac{\log(p)}{p^z},$$ where $P$ denotes the prime zeta function and $\log$ denotes the logarithm.
