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We compute the contribution to the total cross section for the inclusiveproduction of a Standard Model Higgs boson induced by two quarks with differentflavour in the initial state. Our calculation is exact in the Higgs boson massand the partonic center-of-mass energy. We describe the reduction to masterintegrals, the construction of a canonical basis, and the solution of thecorresponding differential equations. Our analytic result contains bothHarmonic Polylogarithms and iterated integrals with additional letters in thealphabet.

Exact N$^3$LO results for $q q^\prime\to H +X$