The harmonic product of δ(x1,..., xn) and δ(x1) and two combinatorial identities
Ya-Qing Li
Abstract
In the framework of nonstandard analysis, Bang-He Li and the author defined the product of any two distributions on Rn via their harmonic representations. The product of δ(x1,..., xn) and δ(x1) was calculated by Kuribayashi and the author in [LK]. In this paper, the result of [LK] is improved to δ(x1,..., xn) δ(x1) =12πρ δ(x1,..., xn) mod infinitesimals where ρ is a positive infinitesimal. Moreover two combinatorial identities are obtained as byproducts.
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