Digamma at z+n

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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