The Abel-Zeilberger Algorithm
Classical Analysis and ODEs
2011-05-03 v1 Combinatorics
Abstract
We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, the Apery-Schmidt-Strehl identity, Calkin's identity and some identities involving Fibonacci numbers.
Cite
@article{arxiv.1105.0178,
title = {The Abel-Zeilberger Algorithm},
author = {William Y. C. Chen and Qing-Hu Hou and Hai-Tao Jin},
journal= {arXiv preprint arXiv:1105.0178},
year = {2011}
}
Comments
18 pages