In this paper, we introduce a new type of degenerate Genocchi polynomials and numbers, which are called degenerate poly-Genocchi polynomials and numbers, by using the degenerate polylogarithm function, and we derive several properties of these polynomials systematically. Then, we also consider the degenerate unipoly-Genocchi polynomials attached to an arithmetic function, by using the degenerate polylogarithm function, and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

中文翻译：

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一类新的具有特定性质的简并多Genocchi多项式

在本文中，我们利用退化的多对数函数引入了一种新型的退化的Genocchi多项式和数，称为退化的poly-Genocchi多项式和数，并系统地推导出了这些多项式的几个性质。然后，我们还通过使用简并多对数函数考虑附加到算术函数的简并单多项式-Genocchi 多项式，并研究这些多项式的一些恒等式。特别是，我们给出了与特殊数和多项式相关的退化单多项式的一些新的显式表达式和恒等式。