  Upper bounds on the Kolmogorov distance (and, equivalently in this case, on
the total variation distance) between the Student distribution with p degrees
of freedom (SD_p) and the standard normal distribution are obtained. These
bounds are in a certain sense best possible, and the corresponding relative
errors are small even for moderate values of p. The same bounds hold on the
closeness between SD_p and SD_q with q>p.
