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B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms
Maciej Rzeszut, Michał Wojciechowski · 2025-07-07 · via math.PR updates on arXiv.org

We prove that B-splines with knots satisfying assumptions of the Berry-Esseen Theorem, which correspond directly to the volumes of sections of the standard simplex, tend to the Gaussian density in any Schwartz seminorm. As a consequence, we derive some asymptotic formulas connecting Hermite and Laguerre polynomials.

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