A $q$-Clausen-Orr type formula and its applications
Combinatorics
2017-04-18 v2 Number Theory
Abstract
We show that certain terminating series can be factorized into a product of two series. As applications we prove a summation formula for a product of two -Delannoy numbers along with some congruences for sums involving -Delannoy numbers. This confirms three recent conjectures of the second author.
Cite
@article{arxiv.1608.02817,
title = {A $q$-Clausen-Orr type formula and its applications},
author = {Hong-Fang Guo and Victor J. W. Guo and Jiang Zeng},
journal= {arXiv preprint arXiv:1608.02817},
year = {2017}
}
Comments
14 pages, accepted by Journal of Mathematical Analysis and Applications