The Abel Lemma and the q-Gosper Algorithm
组合数学
2007-05-23 v1 经典分析与常微分方程
摘要
Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey's bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the sum. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas by using the -Gosper algorithm. It is demonstrated that Abel pairs can be derived from Gosper pairs. This approach applies to many classical summation formulas.
关键词
引用
@article{arxiv.math/0607359,
title = {The Abel Lemma and the q-Gosper Algorithm},
author = {Vincent Y. B. Chen and William Y. C. Chen and Nancy S. S. Gu},
journal= {arXiv preprint arXiv:math/0607359},
year = {2007}
}
备注
17 pages