论文标题
斯特林数字和反阶乘系列
Stirling numbers and inverse factorial series
论文作者
论文摘要
我们研究反阶级系列及其与第一类的史特数字的关系。我们证明了与此类数字的串联函数的特殊表示。使用各种身份对第一类的stirling数字，我们根据系数为特殊数字的反阶段序列构建了许多功能的扩展。这些结果用于证明/否定某些经典功能的渐近扩展。我们还证明了涉及反阶乘的二项式公式。
We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers of the first kind we construct a number of expansions of functions in terms of inverse factorial series where the coefficients are special numbers. These results are used to prove/reprove the asymptotic expansion of some classical functions. We also prove a binomial formula involving inverse factorials.
