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 $A\delta_{0}$ at the en...