Digamma at z+n

From specialfunctionswiki
Revision as of 15:57, 23 June 2016 by Tom (talk | contribs)
Jump to: navigation, search

Theorem

The following formula holds for $n=1,2,3,\ldots$: $$\psi(z+n)=\dfrac{1}{z} + \dfrac{1}{z+1} + \ldots + \dfrac{1}{z+n-1} + \psi(z),$$ where $\psi$ denotes the digamma function.

Proof

References