  We calculate the polarized massive operator matrix element $A_{gq}^{(3)}(N)$
to 3-loop order in Quantum Chromodynamics analytically at general values of the
Mellin variable $N$ both in the single- and double-mass case in the Larin
scheme. It is a transition function required in the variable flavor number
scheme at $O(\alpha_s^3)$. We also present the results in momentum fraction
space.
