2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59315In the framework of nonstandard analysis, Bang-He Li and the author defined the product of any two distributions on $R^n$ via their harmonic representations. The product of $δ(x_{1},..., x_{n})$ and $δ(x_{1})$ was calculated by Kuribayashi and the author in [LK]. In this paper, the result of [LK] is improved to $$δ(x_{1},..., x_{n})\circ δ(x_{1}) =\dfrac{1}{2πρ} δ(x_{1},..., x_{n}) {mod} {infinitesimals}$$ where $ρ$ is a positive infinitesimal. Moreover two combinatorial identities are obtained as byproducts.Latex. To appear in Hiroshima Math. JFunctional AnalysisCombinatoricsLogictext