An algebraic identity on -Apéry numbers

By means of partial fraction decomposition, we establish a q -extension of an algebraic identity on rational function due to Chu [W. Chu, A binomial coefficient identity associated with Beukers’ conjecture on Apéry numbers, The Electronic Journal of Combinatorics 11 (2004) #N15]. Its limiting case as q → 1 leads to a harmonic number identity closely related to Beukers’ well-known conjecture on Apéry numbers.