Difference between revisions of "Bernoulli polynomial and Hurwitz zeta"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$B_n(x)=-n \zeta(1-n,x),...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$B_n(x)=-n \zeta(1-n,x),$$ | $$B_n(x)=-n \zeta(1-n,x),$$ | ||
where $B_n$ denotes the [[Bernoulli B|Bernoulli polynomial]] and $\zeta$ denotes the [[Hurwitz zeta]] function. | where $B_n$ denotes the [[Bernoulli B|Bernoulli polynomial]] and $\zeta$ denotes the [[Hurwitz zeta]] function. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:13, 16 June 2016
Theorem
The following formula holds: $$B_n(x)=-n \zeta(1-n,x),$$ where $B_n$ denotes the Bernoulli polynomial and $\zeta$ denotes the Hurwitz zeta function.
