  We report on the two-loop amplitude computation for the mixed QCD-electroweak
corrections to the process $gg \to Hg$, with exact dependence on the
electroweak boson masses. This amplitude has been employed in the computation
of next-to-leading order (NLO) mixed QCD-electroweak corrections to the
Higgs-boson production rate in arXiv:2010.09451. The master integrals that
appear in the amplitude are evaluated by means of generalized power series
expansions, which allows for fast and high-precision numerical evaluation of
the amplitude in the physical phase-space, proving to be a powerful tool for
phenomenological applications.
