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https://hdl.handle.net/20.500.11851/801
Title: | On Fibonomial Sums Identities With Special Sign Functions: Analytically Q-Calculus Approach | Authors: | Kılıç, Emrah Akkuş, İlker |
Keywords: | Fibonomial coefficients Gaussian q-binomial coefficients Sum identities |
Publisher: | De Gruyter Open Ltd | Source: | Kiliç, E., & Akkus, I. (2018). On Fibonomial sums identities with special sign functions: analytically q-calculus approach. Mathematica Slovaca, 68(3), 501-512. | 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. | URI: | https://doi.org/10.1515/ms-2017-0120 https://hdl.handle.net/20.500.11851/801 |
ISSN: | 0139-9918 |
Appears in Collections: | Matematik Bölümü / Department of Mathematics Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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