Some remarks on an identity of Catalan concerning the Fibonacci numbers
Morgado, José (1980)
Portugaliae mathematica
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Displaying similar documents to “Generalization of identities of Catalan and others”
Some remarks on an identity of Catalan concerning the Fibonacci numbers
Note on some results of A.F. Horadam and A.G. Shannon concerning a Catalan's identity on Fibonacci numbers
Morgado, José (1987)
Portugaliae mathematica
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Gelin-Cesáro identities for Fibonacci and Lucas quaternions
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.
Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Mohammad Farrokhi, D.G. (2009)
Integers
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Octave recurrence relations
Horadam, A.F. (1987)
Portugaliae mathematica
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Generalization of a result of Morgado
Horadam, A.F. (1987)
Portugaliae mathematica
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A generalization of the Cassini formula
Alexey Stakhov (2012)
Visual Mathematics
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Generalization of a result of Hoggatt and Bergum on Fibonacci numbers
Morgado, José (1983-1984)
Portugaliae mathematica
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Fibonacci numbers and Diophantine quadruples: generalizations of results of Morgado and Horadam
Shannon, A.G. (1988)
Portugaliae mathematica
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On binomial sums for the general second order linear recurrence.
Kiliç, Emrah, Tan, Elif (2010)
Integers
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Summation identities for representation of certain real numbers.
Grossman, George, Tefera, Akalu, Zeleke, Aklilu (2006)
International Journal of Mathematics and Mathematical Sciences
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Binomials transformation formulae for scaled Fibonacci numbers
Edyta Hetmaniok, Bożena Piątek, Roman Wituła (2017)
Open Mathematics
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The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.