Difference between revisions of "Integral representation of polygamma 2"

Theorem: The following formula holds: $$\psi^{(m)}(z)=-\displaystyle\int_0^1 \dfrac{t^{z-1}}{1-t} \log^m(t) \mathrm{d}t,$$ where $\psi^{(m)}$ denotes the polygamma and $\log$ denotes the logarithm.