Difference between revisions of "Polygamma series representation"

Theorem: The following formula holds: $$\psi^{(m)}(z)=(-1)^{m+1} m! \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(z+k)^{m+1}},$$ where $\psi^{(m)}$ denotes the polygamma and $m!$ denotes the factorial.