Results 71 to 80 of about 228 (120)

Copper ratio obtained by generalizing the Fibonacci sequence

AIP Advances
In this study, we define a new generalization of the Fibonacci sequence that gives the copper ratio, and we will call it the copper Fibonacci sequence. In addition, inspired by the copper Fibonacci definition, we also define copper Lucas sequences, and ...
Engin Özkan, Hakan Akkuş
doaj   +1 more source

On the Pseudo-Fibonacci and Pseudo-Lucas Quaternions

Electronic Journal of Mathematical Analysis and Applications
Summary: There are a lot of quaternion numbers that are related to the Fibonacci and Lucas numbers or their generalizations have been described and extensively explored. The coefficients of these quaternions have been chosen from terms of Fibonacci and Lucas numbers.
Dişkaya, Orhan, Menken, Hamza
openaire   +2 more sources

Binomial sum formulas from the exponential generating functions of (P, q)−fibonacci and (p, q)−lucas quaternions [PDF]

, 2021
In this paper, we obtain some binomial sum formulas for (p, q)-Fibonacci and (p, q)-Lucas quaternions, by using the exponential generating functions.
Bitim, Bahar Demirtürk, Topal, Nazım
core  

ALGEBRAIC PROPERTIES OF BI-PERIODIC DUAL FIBONACCI QUATERNIONS

, 2019
The purpose of the paper is to construct a new representation of dual quaternions called bi-periodic dual Fibonacci quaternions. These quaternions are originated as a generalization of the known quaternions in literature such as dual Fibonacci ...
Ekmekci, N., Gok, I, Ates, F.
core  

q-Fibonacci bicomplex quaternions

, 2021
In the paper, we define the $q$-Fibonacci bicomplex quaternions and the $q$-Lucas bicomplex quaternions, respectively. Then, we give some algebraic properties of $q$-Fibonacci bicomplex quaternions and the $q$-Lucas bicomplex quaternions.
openaire   +4 more sources

On quaternions with generalized Fibonacci and Lucas number components

, 2015
In this paper, we give the exponential generating functions for the generalized Fibonacci and generalized Lucas quaternions, respectively.
Emrah Polatli, Emrah Polatlı, Seyhun Kesim   +2 more
core   +1 more source

More identities for Fibonacci and Lucas quaternions

, 2020
In this paper, we define the associate matrix as% \begin{equation*} F=\left( \begin{array}{cc} 1+i+2j+3k & i+j+2k \\ i+j+2k & 1+j+k% \end{array}% \right) . \end{equation*}% By the means of the matrix F , we give several identities
Irmak, Nurettin
core  

On (p, q)-Fibonacci quaternions and their Binet formulas, generating functions and certain binomial sums

, 2017
WOS:000401669000029Formulas and sums involving many well-known special quaternion sequences (such as the Fibonacci, Pell, Jacobsthal quaternion sequences and so on) play important roles in various branches of science. Binet formulas, generating functions
İpek, Ahmet
core   +1 more source

A study on circular-hyperbolic Fibonacci and Lucas quaternions

, 2021
We investigate some properties of circular-hyperbolic Fibonacci and Lucas quaternions (CHF LQ for short). Also, we introduce their negative subscripts and obtain combinatorial sums.
Yılmaz, Nazmiye
core  

Some unrestricted Fibonacci and Lucas hyper-complex numbers

, 2020
A number of studies have investigated the Fibonacci quaternions and octonions that include consecutive terms of the Fibonacci sequence. This paper presents a new generalization of Fibonacci quaternions, octonions and sedenions, where non-consecutive ...
Daşdemir, Ahmet, Bilgici, Göksal
core   +1 more source