English

A $q$-Clausen-Orr type formula and its applications

Combinatorics 2017-04-18 v2 Number Theory

Abstract

We show that certain terminating 6ϕ5_{6}\phi_5 series can be factorized into a product of two 3ϕ2_{3}\phi_{2} series. As applications we prove a summation formula for a product of two qq-Delannoy numbers along with some congruences for sums involving qq-Delannoy numbers. This confirms three recent conjectures of the second author.

Keywords

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

R2 v1 2026-06-22T15:15:56.341Z