Difference between revisions of "Relation between polygamma and Hurwitz zeta"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\psi^{(m)}(z)=(-1)^{m+1} m! \zeta(m+1,z),$$ where $\psi^{(m)}$ de...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\psi^{(m)}(z)=(-1)^{m+1} m! \zeta(m+1,z),$$ | $$\psi^{(m)}(z)=(-1)^{m+1} m! \zeta(m+1,z),$$ | ||
where $\psi^{(m)}$ denotes the [[polygamma]] and $\zeta$ denotes the [[Hurwitz zeta]] function. | where $\psi^{(m)}$ denotes the [[polygamma]] and $\zeta$ denotes the [[Hurwitz zeta]] function. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 06:34, 11 June 2016
Theorem
The following formula holds: $$\psi^{(m)}(z)=(-1)^{m+1} m! \zeta(m+1,z),$$ where $\psi^{(m)}$ denotes the polygamma and $\zeta$ denotes the Hurwitz zeta function.
