A q-Clausen-Orr type formula and its applications

2016/08/09 by Guo, Hong-Fang, Guo, Victor J. W., Zeng, Jiang
#05A10 #05A30 #11B65 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1608.02817

Abstract

We show that certain terminating ₆ϕ₅ series can be factorized into a product of two ₃ϕ₂ series. As applications we prove a summation formula for a product of two q-Delannoy numbers along with some congruences for sums involving q-Delannoy numbers. This confirms three recent conjectures of the second author.

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