The aim of this paper is to study the complete and incomplete degenerate Bell polynomials, which are degenerate versions of the complete and incomplete Bell polynomials, and to derive some properties and identities for those polynomials. In particular, we introduce some new polynomials associated with the incomplete degenerate Bell polynomials. In fact, they are the coefficients of the reciprocal of the power series given by 1 plus the one appearing as the exponent of the generating function of the complete degenerate Bell polynomials.

中文翻译：

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完全和不完全退化贝尔多项式的一些新公式

本文的目的是研究完全和不完全退化贝尔多项式，它们是完全和不完全贝尔多项式的退化版本，并推导出这些多项式的一些性质和恒等式。特别是，我们引入了一些与不完全退化贝尔多项式相关的新多项式。事实上，它们是由 1 给出的幂级数的倒数加上作为完全退化贝尔多项式的生成函数的指数出现的系数。