Let $Z : = \{ (x, y) \in \mathbb{C} : x > 0 \}$ be the D3740: Complex open right half-plane such that

(i)	$\Gamma : Z \to \mathbb{C}$ is the D258: Gamma function

The digamma function is the D4881: Complex function \begin{equation} Z \to \mathbb{C}, \quad z \mapsto \frac{d}{d z} \log \Gamma (z) \end{equation}