Difference between revisions of "Integral representation of polygamma 2"
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| − | <strong>[[Integral representation of polygamma 2|Theorem]]:</strong> The following formula holds: | + | <strong>[[Integral representation of polygamma 2|Theorem]]:</strong> The following formula holds for $\mathrm{Re}(z)>0$ and $m>0$: |
$$\psi^{(m)}(z)=-\displaystyle\int_0^1 \dfrac{t^{z-1}}{1-t} \log^m(t) \mathrm{d}t,$$ | $$\psi^{(m)}(z)=-\displaystyle\int_0^1 \dfrac{t^{z-1}}{1-t} \log^m(t) \mathrm{d}t,$$ | ||
where $\psi^{(m)}$ denotes the [[polygamma]] and $\log$ denotes the [[logarithm]]. | where $\psi^{(m)}$ denotes the [[polygamma]] and $\log$ denotes the [[logarithm]]. | ||
