  We calculate the unpolarized twist-2 three-loop splitting functions
$P_{qg}^{(2)}(x)$ and $P_{gg}^{(2,\rm N_F)}(x)$ and the associated anomalous
dimensions using massive three-loop operator matrix elements. While we
calculate $P_{gg}^{(2,\rm N_F)}(x)$ directly, $P_{qg}^{(2)}(x)$ is computed
from 1200 even moments, without any structural prejudice, using a hierarchy of
recurrences obtained for the corresponding operator matrix element. The largest
recurrence to be solved is of order 12 and degree 191. We confirm results in
the foregoing literature.
