Abstract

In this study we introduce a second type of higher order generalized geometric polynomials. This we achieve by examining the generalized stirling numbers S(n, k, α, β, γ) [Hsu and Shiue, 1998] for some negative arguments. We study their number theoretic properties, asymptotic properties, and their combinatorial properties using the notion of barred preferential arrangements. We also proposed a generalisation of the classical Euler polynomials and show how these generalized Euler polynomials are related to the second type of higher order generalized geometric polynomials.

中文翻译：

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第二类高阶广义几何多项式和高阶广义欧拉多项式

摘要

在这项研究中，我们介绍了第二种高阶广义几何多项式。我们通过检查广义斯特林数S ( n, k, α, β, γ ) [Hsu and Shiue, 1998] 来实现一些否定论点。我们使用禁止优先安排的概念研究它们的数论性质、渐近性质和组合性质。我们还提出了经典欧拉多项式的泛化，并展示了这些泛化欧拉多项式与第二类高阶广义几何多项式的关系。