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We calculate the massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-looporder in Quantum Chromodynamics at general values of the Mellin variable $N$.This is the first complete transition function needed in the variable flavornumber scheme obtained at $O(\alpha_s^3)$. A first independent recalculation isperformed for the contributions $\propto N_F$ of the 3-loop anomalous dimension$\gamma_{gq}^{(2)}(N)$.

The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number Scheme at O(\alpha_s^3)