Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

Abstract

In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of Heine’s transformation, the q-Pfaff–Saalschutz theorem and the q-Kummer sum. Consequently several identities for generalized Fibonomial–Lucanomial coefficients are obtained by specifying the parameter p and the base q. © 2018 Springer Science+Business Media, LLC, part of Springer Nature