Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1804-42
Keywords
Formal residue, extended Zeilberger algorithm, Stirling number
First Page
2466
Last Page
2480
Recommended Citation
HAITAO, JIN
(2018)
"Formal residue and computer-assisted proofs of combinatorial identities,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 29.
https://doi.org/10.3906/mat-1804-42
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/29
