Analytic Reconstruction of heavy-quark two-point functions at O(αₛ³)

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Using a method previously developed, based on the Mellin-Barnes transform, we reconstruct the two-point correlators in the vector, axial, scalar and pseudoscalar channels from the Taylor expansion at q²=0, the threshold expansion at q²=4m² and the OPE at q²→ -∞, where m is the heavy quark mass. The reconstruction is analytic and systematic and is controlled by an error function which becomes smaller as more terms in those expansions are known.