View source for Value of polygamma at positive integer

==Theorem==
The following formula holds for $n=1,2,\ldots$:
$$\psi^{(m)}(n+1)=(-1)^m m! \left[ -\zeta(m+1)+1 + \dfrac{1}{2^{m+1}}+\ldots + \dfrac{1}{n^{m+1}} \right],$$
where $\psi^{(m)}$ denotes the [[polygamma]], $m!$ denotes the [[factorial]], and $\zeta(m+1)$ denotes the [[Riemann zeta]].
==Proof==

==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Value of polygamma at 1|next=Value of polygamma at 1/2}}: $6.4.3$

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