Difference between revisions of "Polygamma recurrence relation"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</strong> The following formula holds: $$\psi^{(m)}(z+1)=\psi^{(m)}(z)+\...") |
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\psi^{(m)}(z+1)=\psi^{(m)}(z)+\dfrac{(-1)^mm!}{z^{m+1}},$$ | $$\psi^{(m)}(z+1)=\psi^{(m)}(z)+\dfrac{(-1)^mm!}{z^{m+1}},$$ | ||
where $\psi^{(m)}$ denotes the [[polygamma]] and $m!$ denotes the [[factorial]]. | where $\psi^{(m)}$ denotes the [[polygamma]] and $m!$ denotes the [[factorial]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Revision as of 06:32, 11 June 2016
Theorem
The following formula holds: $$\psi^{(m)}(z+1)=\psi^{(m)}(z)+\dfrac{(-1)^mm!}{z^{m+1}},$$ where $\psi^{(m)}$ denotes the polygamma and $m!$ denotes the factorial.
