On Fibonomial sums identities with special sign functions: analytically q-calculus approach

Abstract

Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809-818] presented interesting two sum identities including the Fibonomial coefficients and Fibonacci numbers. These sums are unusual as they include a rare sign function and their upper bounds are odd. In this paper, we give generalizations of these sums including the Gaussian q-binomial coefficients. We also derive analogue q-binomial sums whose upper bounds are even. Finally we give q-binomial sums formulæ whose weighted functions are different from the earlier ones. To prove the claimed results, we analytically use q-calculus.