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

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