View source for Integral representation of polygamma for Re(z) greater than 0

==Theorem==
The following formula holds for $\mathrm{Re}(z)>0$ and $m>0$:
$$\psi^{(m)}(z)=(-1)^{m+1} \displaystyle\int_0^{\infty} \dfrac{t^m e^{-zt}}{1-e^{-t}} \mathrm{d}t,$$
where $\psi^{(m)}$ denotes the [[polygamma]] and $e^{-zt}$ denotes the [[exponential]].

==Proof==

==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Polygamma|next=Value of polygamma at 1}}: $6.4.1$

[[Category:Theorem]]
[[Category:Unproven]]