Sums of products of two Gaussian $q$-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.
Gaussian $q$-binomial coefficients, Fibonomial coefficients, Lucanomial coefficients, sum identities
KILIÇ, EMRAH and PRODINGER, HELMUT
"Evaluation of sums involving products of Gaussian $q$-binomial coefficients with applications to Fibonomial sums,"
Turkish Journal of Mathematics: Vol. 41:
3, Article 20.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss3/20