- Turkish Journal of Mathematics
- Vol: 42 Issue: 5
- Formal residue and computer-assisted proofs of combinatorial identities
Formal residue and computer-assisted proofs of combinatorial identities
Authors : Jin Haitao
Pages : 2466-2480
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :The coefficient of $x^{-1}$ of a formal Laurent series $f(x)$ is called the formal residue of $f(x)$. Many combinatorial numbers can be represented by the formal residues of hypergeometric terms. With these representations and the extended Zeilberger algorithm, we generate recurrence relations for summations involving combinatorial sequences such as Stirling numbers and their $q$-analog. As examples, we give computer proofs of several known identities and derive some new identities. The applicability of this method is also studied.Keywords : Formal residue, extended Zeilberger algorithm, Stirling number