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

We calculate the massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$. This is the first complete transition function needed in the variable flavor number scheme obtained at $O({\alpha }_s^3)$. A first independent recalculation is performed for the contributions $\propto N_F$ of the 3-loop anomalous dimension ${\gamma }_{gq}^{(2)}(N)$.