The aim of this work is to find “good” approximations to the Digamma function Ψ. We construct an infinite family of “basic” functions {Ia, a ∈ [0, 1]} covering the Digamma function. These functions are shown to approximate Ψ locally and asymptotically, and that for any x ∈ R, there exists a such that Ψ (x) = Ia (x). Local and global bounding error functions are found and, as a consequence, new ...
