A WZ proof of a “curious” identity.
Ekhad, Shalosh B., Mohammed, Mohamud (2003)
Integers
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Ekhad, Shalosh B., Mohammed, Mohamud (2003)
Integers
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Ahmet Daşdemir (2019)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan's identity for the Lucas quaternions.
P. Anandani (1969)
Annales Polonici Mathematici
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Robert Bartoszyński (1974)
Colloquium Mathematicae
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Andrews, George E. (1996)
The Electronic Journal of Combinatorics [electronic only]
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Paule, Peter (1994)
The Electronic Journal of Combinatorics [electronic only]
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Kauers, Manuel, Schneider, Carsten (2008)
The Electronic Journal of Combinatorics [electronic only]
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Kiliç, Emrah, Tan, Elif (2010)
Integers
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Prodinger, Helmut (2008)
Integers
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Bijan Kumar Patel, Prasanta Kumar Ray (2021)
Communications in Mathematics
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The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.
Lengyel, Tamás (2007)
Integers
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Bhatnagar, Gaurav (2011)
The Electronic Journal of Combinatorics [electronic only]
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Mohammad Farrokhi, D.G. (2009)
Integers
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V. Mandekić-Botteri (1986)
Matematički Vesnik
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