Difference between revisions of "Derivative of zeta at -1"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Proposition:</strong> The following formula holds: $$\zeta'(-1)=\dfrac{1}{12}-\log(A...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\zeta'(-1)=\dfrac{1}{12}-\log(A),$$ | $$\zeta'(-1)=\dfrac{1}{12}-\log(A),$$ | ||
where $\zeta$ denotes the [[Riemann zeta function]], $A$ denotes the [[Glaisher–Kinkelin constant]], and $\log$ denotes the [[logarithm]]. | where $\zeta$ denotes the [[Riemann zeta function]], $A$ denotes the [[Glaisher–Kinkelin constant]], and $\log$ denotes the [[logarithm]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 20:20, 20 June 2016
Theorem
The following formula holds: $$\zeta'(-1)=\dfrac{1}{12}-\log(A),$$ where $\zeta$ denotes the Riemann zeta function, $A$ denotes the Glaisher–Kinkelin constant, and $\log$ denotes the logarithm.
