On binomial sums for the general second order linear recurrence.

Kiliç, Emrah; Tan, Elif

Displaying similar documents to “On binomial sums for the general second order linear recurrence.”

Generalization of an identity involving the generalized Fibonacci numbers and its applications.

Mohammad Farrokhi, D.G. (2009)

Integers

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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.

A WZ proof of a “curious” identity.

Ekhad, Shalosh B., Mohammed, Mohamud (2003)

Integers

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Algebraic relations for reciprocal sums of Fibonacci numbers

Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2007)

Acta Arithmetica

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A generalization of the Cassini formula

Alexey Stakhov (2012)

Visual Mathematics

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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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An inequality for Fibonacci numbers

Horst Alzer, Florian Luca (2022)

Mathematica Bohemica

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We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.

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.

Jensen proof of a curious binomial identity.

Chu, Wenchang, Di Claudio, Leontina Veliana (2003)

Integers

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On Balancing and Lucas-balancing Quaternions

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.