The harmonic product of δ (x1,..., xn) and δ (x1) and two combinatorial identities
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) =12π δ (x1,..., xn) mod infinitesimals where is a positive infinitesimal. Moreover two combinatorial identities are obtained as byproducts.
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