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We compute the next-to-leading virtual QCD corrections to the partonic crosssection of the production of a Higgs boson in association with a $Z$ boson ingluon fusion. The calculation is based on the recently introduced method ofevaluating the amplitude via an expansion in terms of a small transversemomentum. We generalize the method to the case of different masses in the finalstate and of a process not symmetric in the forward-backward directionexchange. Our analytic approach gives a very good approximation (better thanpercent) of the partonic cross section in the center of mass energy region upto $\sim 750 \,\textrm{GeV}$, where at the LHC $\sim 98\%$ of the totalhadronic cross section is concentrated.

Virtual corrections to $gg\to ZH$ via a transverse momentum expansion