Difference between revisions of "Value of polygamma at 1"

From specialfunctionswiki
Jump to: navigation, search
(Created page with "==Theorem== The following formula holds: $$\psi^{(m)}(1)=(-1)^{m+1} m! \zeta(m+1),$$ where $\psi^{(m)}$ denotes the polygamma, $m!$ denotes the factorial$, and $\zeta$...")
(No difference)

Revision as of 08:08, 11 June 2016

Theorem

The following formula holds: $$\psi^{(m)}(1)=(-1)^{m+1} m! \zeta(m+1),$$ where $\psi^{(m)}$ denotes the polygamma, $m!$ denotes the factorial$, and $\zeta$ denotes the Riemann zeta function.

Proof

Reference

Retrieved from "http://specialfunctionswiki.org/index.php?title=Value_of_polygamma_at_1&oldid=6105"