The Abel Lemma and the q-Gosper Algorithm
Vincent Y. B. Chen, William Y. C. Chen, Nancy S. S. Gu
Abstract
Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey's 6ψ6 bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the 6ψ6 sum. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas by using the q-Gosper algorithm. It is demonstrated that Abel pairs can be derived from Gosper pairs. This approach applies to many classical summation formulas.
Create a lesson
Related papers
Graded Ehrhart theory for hypersimplices
Nathaniel Libman, Weston Miller
Closing the gap and settling the problem of queens on an n× n board, each attacking at most one other
Kristina Ago, Bojan Bašić, Radojka Ciganović
Leading term strandings for webs
Michael Bo, Madelyn Burns, Junyang Chen et al.
Refutation of the Non-Cancelling-Intersections Conjecture
Hermann Wilhelm
Asymptotic Bounds for Online Ramsey Numbers of Stars versus Long Paths and Cycles
Sam Beilis, Israel R. Curbelo, Elizabeth R. Koizumi
The Erdos--Gallai bound for consecutive even cycle lengths
Yaobin Chen, Hong Liu, Xia Wang et al.