Studying degenerate versions of various special polynomials has became an active area of research and has yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of the polylogarithm function, the so-called degenerate polylogarithm function. Then we construct a new type of degenerate Bernoulli polynomial and number, the so-called degenerate poly-Bernoulli polynomial and number, by using the degenerate polylogarithm function, and derive several properties concerning the degenerate poly-Bernoulli numbers.

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关于一种新的简并伯努利数的注记

研究各种特殊多项式的简并形式已经成为研究的活跃领域，并产生了许多有趣的算术和组合结果。在这里，我们介绍了多对数函数的简并形式，即所谓的简并多对数函数。然后，我们利用简并对数函数构造了一种新的简并伯努利多项式和数，即所谓简并伯努利多项式和数，并推导了有关简并伯努利数的几个性质。