Definition: The term "digamma function" is derived from the Greek word "digama," which means "infinite." The digamma function, denoted by $\psi(x)$ or $\psi(x)^\prime$, is defined as: $$\psi(x) = \frac{1}{x} + \sum_{n=2}^{\infty}\left(\frac{x}{n}-\frac{1}{(n+1)x}\right)\tag{1}$$
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