| 唐志华,徐沥泉.论一种用到Howard广义斯特灵数的求和公式[J].数学研究及应用,2010,30(6):992~996 |
| 论一种用到Howard广义斯特灵数的求和公式 |
| On a Kind of Summation Formula Using Howard's Generalized Stirling Numbers |
| 投稿时间：2009-01-15 修订日期：2009-06-30 |
| DOI：10.3770/j.issn:1000-341X.2010.06.006 |
| 中文关键词: 广义阶乘 Howard 广义斯特灵数 级数变换公式 形式级数求和法. |
| 英文关键词:generalized factorial Howard's GSN series-transformation formula formal series summation. |
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| 中文摘要: |
| 基于文献[2]和[4]的研究结果,借助于一个级数变换公式,得到了一个新的形式级数恒等式,用它可以推导出包括广义斯特灵数、贝尔数和欧拉公式等等在内的许多新旧恒等式. |
| 英文摘要: |
| It is shown that Howard's degenerate weighted Stirling numbers can be used to construct a fruitful summation formula for a class of formal power series involving generalized factorials. This is achieved with the aid of a series-transformation formula due to He, Hsu and Shiue, and several identities involving generalized Stirling numbers and Bell numbers are given to illustrate the application of the formula obtained. |
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