| 与中心数相关的一类级数求和公式 |
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| 引用本文： | 徐利治,马欣荣. 与中心数相关的一类级数求和公式[J]. 数学研究及应用, 2014, 34(1): 1-11 |
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| 作者姓名： | 徐利治 马欣荣 |
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| 作者单位： | 大连理工大学数学科学学院,辽宁 大连 116024;苏州大学数学科学学院, 江苏 苏州 215006 |
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| 基金项目： | 国家自然科学基金 (Grant No.11071183). |
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| 摘 要： | This paper provides a pair of summation formulas for a kind of combinatorial series involvingak＋b m as a factor of the summand. The construction of formulas is based on a certain series transformation formula [2, 7, 9] and by making use of the C-numbers [3]. Various consequences and examples including several remarkable classic identities are presented to illustrate some applications of the formulas obtained.
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| 关 键 词： | 级数求和 变换公式 数学 数论 |
| 收稿时间： | 2012-10-18 |
| 修稿时间： | 2013-07-09 |
On a Kind of Series Summation Utilizing $C$-Numbers |
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| Leetsch C. HSU and Xinrong MA. On a Kind of Series Summation Utilizing $C$-Numbers[J]. Journal of Mathematical Research with Applications, 2014, 34(1): 1-11 |
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| Authors: | Leetsch C. HSU and Xinrong MA |
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| Affiliation: | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China;School of Mathematical Sciences, Soochow University, Jiangsu 215006, P. R. China |
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| Abstract: | This paper provides a pair of summation formulas for a kind of combinatorial series involving $binom{ak+b}{m}$ as a factor of the summand. The construction of formulas is based on a certain series transformation formula [2,,7,,9] and by making use of the $C$-numbers [3]. Various consequences and examples including several remarkable classic identities are presented to illustrate some applications of the formulas obtained. |
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| Keywords: | combinatorial series summation formula difference operator generalized Stirling number $C$-number. |
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