Let ψ denote the psi (or digamma) function. We determine the values of theparameters p, q and r such that ψ(n) ≈ ln(n + p) - <img border=0 width=32 height=32 src="../../../../../img/revistas/cam/v31n1/a05img01.jpg" align=absmiddle> is the best approximations. Also, we present closer bounds for psi function, which sharpens some known results due to Muqattash and Yahdi, Qi and Guo, and Mortici. Mathematical subject classification: 33B15, 26D15.
psi function; polygamma functions; rate of convergence; approximations
