广义Cauchy数的一些恒等式

广义Cauchy数的一些恒等式

李志荣¹, 肖冰², 袁文俊³

1. 中山火炬职业技术学院信息工程系, 广东中山 528436; 2. 新疆师范大学数学系, 乌鲁木齐 830054;3. 广州大学数学与信息科学学院, 广州 510006

收稿日期:2008-02-23 修回日期:1900-01-01 出版日期:2009-01-26 发布日期:2009-01-26
通讯作者: 袁文俊

Some Identities Related to the Generalized Cauchy Numbers

LI Zhirong¹, XIAO Bing², YUAN Wenjun³

1. Department of Information Engineering, Zhongshan Torch College, Zhongshan 528436, Guangdong Province, China;2. Department of Mathematics, Xinjiang Normal University, Urumuqi 830054, China；3. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Received:2008-02-23 Revised:1900-01-01 Online:2009-01-26 Published:2009-01-26
Contact: YUAN Wenjun

摘要/Abstract

摘要： 利用Stirling数给出广义Cauchy数的显式计算公式, 并讨论其分别与Stirling数、 Bernoulli数和Euler数之间的关系, 得到了包含广义Cauchy数的一些恒等式, 并改进了已有的卷积公式.

关键词: 广义Cauchy数, Stirling数, Bernoulli数, Euler数, 发生函数

Abstract: An explicit computational formula of the generalized Cauchy numbers was given by means of the Stirling numbers, and then the relationships of the explicit computational formula with each of the Stirling numbers, Bernoulli numbers and Euler numbers were discussed, and some identities involving the Cauchy numbers were obtained. At last, we also improved the convolution formula which has been given.

Key words: generalized Cauchy number, Stirling number, Bernoul li number, Euler number, generating function

中图分类号:

O157.1

李志荣, 肖冰, 袁文俊. 广义Cauchy数的一些恒等式[J]. J4, 2009, 47(01): 17-20.

LI Zhirong, XIAO Bing, YUAN Wenjun. Some Identities Related to the Generalized Cauchy Numbers[J]. J4, 2009, 47(01): 17-20.