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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 anomalousdimensions using massive three-loop operator matrix elements. While wecalculate $P_{gg}^{(2,\rm N_F)}(x)$ directly, $P_{qg}^{(2)}(x)$ is computedfrom 1200 even moments, without any structural prejudice, using a hierarchy ofrecurrences obtained for the corresponding operator matrix element. The largestrecurrence to be solved is of order 12 and degree 191. We confirm results inthe foregoing literature.

The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, N_F)}$