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B-splines approximate the Gaussian density and Hermite functions in Schwartz seminorms (2507.04507v1)
Published 6 Jul 2025 in math.PR and math.CA
Abstract: 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.