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

Exact bounds on the closeness between the Student and standard normal distributions