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Mehler--Heine asymptotics for finite differences of mass-modified Charlier and Meixner polynomials
Point-mass perturbations and finite-difference operations alter the finite-degree structure of discrete orthogonal polynomials, but their combined effect at the Mehler--Heine scale is not immediate. We study the monic Charlier and Meixner families under a pure Uvarov modification by a fixed mass $Aδ
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