The digamma function

Γ′(x) Γ(x)

. (10.1.1)

Here Γ(x) is the gamma function defined by

Γ(x) =

tx−1e−t dt. (10.1.2)

Many of the analytic properties can be derived from those of Γ(x). The next theorem represents a collection of the important properties of Γ(x) that are used in the current paper. The reader will find in [22] detailed proofs.