Results 141 to 150 of about 1,044,414 (185)

A New Polar Representation and Identities for Split Leonardo Quaternions

Mathematical methods in the applied sciences
In this study, we define split Leonardo quaternion sequences with components involving Leonardo numbers. We give fundamental properties and identities associated with split Leonardo quaternions, such as Binet's formula, as well as identities attributed ...
Ali Atasoy
semanticscholar   +1 more source

A Study On Gaussian Generalized Edouard Numbers

Asian Journal of Advanced Research and Reports
This paper examines the properties and applications of Gaussian Generalized Edouard numbers, aiming to enrich the theoretical framework of number sequences. Utilizing analytical and algebraic techniques, we derive novel recurrence relations, sum formulas,
Emine Esra Ayrılma, Y. Soykan
semanticscholar   +1 more source

Extended Generalized Fibonacci and Tribonacci Polynomials with some Properties

Sarajevo Journal of Mathematics
In this paper, we introduced the extended generalized Fibonacci polynomial sequence \{$Y_{2,n}$\} and extended generalized Tribonacci polynomial \{$Y_{3,n}$\} with arbitrary initial values and established a recursive matrix and then presented some ...
Vaishali Billore, Naresh Patel, Hemant Makwana   +2 more
semanticscholar   +1 more source

Two-periodic ternary recurrences and their Binet-formula

2012
The two-periodic ternary recurrence sequence is defined by relations \(\gamma _n=a\gamma _{n-1}+b\gamma _{n-2}+c\gamma _{n-3}\) if \(n\) is even and \(\gamma _n=d\gamma _{n-1}+e\gamma _{n-2}+f\gamma _{n-3}\) if \(n\) is odd. In this paper, Cooper's approach [\textit{C. Cooper}, Congr.
Alp , M, Irmak , N, Szalay, László
openaire   +3 more sources

A bijective proof of generalized Cauchy–Binet, Laplace, Sylvester and Dodgson formulas

Linear and Multilinear Algebra, 2020
In this paper, we give the generalization of Cauchy–Binet, Laplace, Sylvester and generalized Dodgson's condensation formulas for the case of rectangular determinants.
openaire   +1 more source

QUANTITATIVE GROWTH OF LINEAR RECURRENCES

Journal of the Australian Mathematical Society
Let $\{u_n\}_n$ be a nondegenerate linear recurrence sequence of integers with Binet’s formula given by ${u_n= \sum _{i=1}^{m} P_i(n)\alpha _i^n.}$ Assume $\max _i \vert \alpha _i \vert>1$ .
Armand Noubissie
semanticscholar   +1 more source

ON GAUSSIAN FUZZY LUCAS NUMBERS

Journal of Science and Arts
In the present paper, we introduce a new class of fuzzy numbers, which we will call Gaussian fuzzy Lucas numbers. We establish some fundamental properties and identities for these newly defined numbers, including the recurrence relation, Binet’s formula,
Tülay Yaǧmur
semanticscholar   +1 more source

On Leonardo Octonions

Journal of Information & Optimization Sciences
In this article, we give a new family of Octonions. We describe the Leonardo Octonions. Then, we derive certain algebraic characteristics for Leonardo Octonions including the generating function, Binet’s formula, exponential generating function, some ...
Hayrullah Özimamoğlu, Paula Catarino
semanticscholar   +1 more source

A new member of the Pell sequences: the pseudo-Pell sequence

Studia Universitatis Babeş-Bolyai. Mathematica
In this study, we define a new family of the Pell numbers and establish some properties of the relation to the ordinary Pell numbers. We give some identities the pseudo-Pell numbers.
Hasan Gökbaş
semanticscholar   +1 more source

Fibonacci Polynomials and It’s Generalization

Mikailalsys Journal of Mathematics and Statistics
This article explores the definition, properties, and generalizations of Fibonacci polynomials, providing a comprehensive understanding of their mathematical significance.
Nand Kishor Kumar, S.K. Sahani
semanticscholar   +1 more source