| On a Kind of Series Summation Utilizing $C$-Numbers |
| Received:October 18, 2012 Revised:July 09, 2013 |
| Key Words:
combinatorial series summation formula difference operator generalized Stirling number $C$-number.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071183). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.01.001 |
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