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Gluon fusion processes like single and double Higgs production exhibit slowconvergence and pose severe computational challenges. We show how the top-quarkmass dependence of the virtual amplitudes can be reconstructed with a conformalmapping and Pad\'e approximants based on the expansion in the inverse top-quarkmass and the non-analytic terms in the expansion around the top threshold. Themethod is then applied at two- and three-loop order.

Pad\'e approach to top-quark mass effects in gluon fusion amplitudes