  Sequences of algebraic upper and lower bounds on the Wallis ratio are given
with the relative errors that converge to 0 geometrically and uniformly on any
interval of the form [x_0,\infty) for x_0>-\frac12; moreover, the relative and
absolute errors converge to 0 as x\to\infty. These conclusions are based on
corresponding results for the digamma function \psi:=\Ga'/\Ga. Relations with
other relevant results are discussed, as well as the corresponding
computational aspects. This work was motivated by studies of exact bounds
involving the Student probability distribution.
