$δ(x_{1},..., x_{n})$和PDMATHAAB的调和积与两个组合恒等式
The harmonic product of $δ(x_{1},..., x_{n})$ and $δ(x_{1})$ and two combinatorial identities
摘要：
在非标准分析的框架下，李邦和等人通过调和表示定义了$R^n$上任意两个分布的乘积。Kuribayashi和作者在[LK]中计算了$δ(x_{1},..., x_{n})$和$δ(x_{1})$的乘积。本文将[LK]的结果改进为$$δ(x_{1},..., x_{n})\circ δ(x_{1}) =\dfrac{1}{2πρ} δ(x_{1},..., x_{n}) {mod} {infinitesimals}$$，其中$ρ$为正无穷小.此外，两个组合身份得到的副产品。
英文摘要：
In 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
