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

In: Mathematica Slovaca, vol. 68, no. 3
Emrah Kiliç - Ilker Akkus
Detaily:
Rok, strany: 2018, 501 - 512
Kľúčové slová:
Fibonomial coefficients, Gaussian $q$-binomial coefficients, sum identities
O článku:
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 \emph{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 formul\ae whose weighted functions are different from the earlier ones. To prove the claimed results, we analytically use $q$-calculus.
Ako citovať:
ISO 690:
Kiliç, E., Akkus, I. 2018. On Fibonomial sums identities with special sign functions: analytically $q$-calculus approach. In Mathematica Slovaca, vol. 68, no.3, pp. 501-512. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0120

APA:
Kiliç, E., Akkus, I. (2018). On Fibonomial sums identities with special sign functions: analytically $q$-calculus approach. Mathematica Slovaca, 68(3), 501-512. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0120
O vydaní: