Results 21 to 30 of about 14,002 (132)

Arctangent Identities Involving the Jacobsthal and Jacobsthal-Lucas Numbers

Electronic Journal of Mathematical Analysis and Applications
This study presents novel arctangent identities that establish connections between the Jacobsthal and Jacobsthal-Lucas numbers. These findings contribute to the understanding of the interplay between trigonometric functions and number theory, particularly in relation to well-known mathematical sequences and constants.
Orhan Dişkaya
semanticscholar   +3 more sources

A New Approach to k-Jacobsthal Lucas Sequences [PDF]

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2021
In this study, 〖CS〗_(k,n) of S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas sequences is defined. S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas S_(k,n) sequences is obtained.In addition the transformation of CS_(k,n) is written as the ...
Hakan Akkuş, Engin Özkan, Rabia Nagehan Üregen   +2 more
doaj   +2 more sources

On k-circulant matrices involving the Jacobsthal-Lucas numbers

Hacettepe Journal of Mathematics and Statistics
Let k be a nonzero complex number. In this paper, we consider a k-circulant matrix whose first row is (j_{1},j_{2},...,j_{n}), where j_{n} is the n^{th} Jacobsthal-Lucas number. The formulae for the eigenvalues of such matrix are obtained.
Biljana Radičić
semanticscholar   +2 more sources

Solutions of a Markoff type equation in the Jacobsthal- Lucas numbers

Boletim da Sociedade Paranaense de Matemática
Let $\{j_n\}_{n\geq0}$ be the sequence of Jacobsthal- Lucas number, that is given by the relation $j_0=2$, $j_1=1$, $j_n=j_{n-1}+2j_{n-2}$ for all $n\geq2$.
Qasim N. Alabrahimi, H. Hashim
semanticscholar   +2 more sources

Introduction to Third-Order Jacobsthal and Modified Third-Order Jacobsthal Hybrinomials [PDF]

Discussiones Mathematicae - General Algebra and Applications, 2021
The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we introduce and study the third-order Jacobsthal and modified third-order Jacobsthal hybrinomials, i.e., polynomials, which are a generalization of the ...
Cerda-Morales Gamaliel
doaj   +2 more sources

Gaussian Jacobsthal And Gaussian Jacobsthal Lucas Numbers. [PDF]

Ars Comb., 2013
In this study we define and study the Gaussian Jacob-sthal and Gaussian Jacobsthal Lucas numbers. We give generating functions, Binet formulas, explicit formulas and Q matrix of these numbers. We also present explicit combinatorial and determinantal expressions, study negatively subscripted numbers and give various identities. Similar to the Jacobsthal
Aşçı, Mustafa, Gürel, Eşref
openaire   +5 more sources

Non-Newtonian Jacobsthal and Jacobsthal-Lucas numbers: A new look

Filomat
In this study, we introduce a novel version of Jacobsthal and Jacobsthal-Lucas numbers, termed as non-Newtonian Jacobsthal and non-Newtonian Jacobsthal-Lucas numbers. We investigate various char-acteristics of these newly defined sequences. Additionally,
İlknur Yeşilyurt, Nilay Değirmen
semanticscholar   +2 more sources

On the bi-periodic k-Jacobsthal and k-Jacobsthal-Lucas numbers

Progress in Applied Science and Technology
This paper introduces and investigates the bi-periodic Jacobsthal and Jacobsthal–Lucas sequences, extending the classical Jacobsthal framework by incorporating periodicity and a tunable parameter .
M. Tatong, O. Sthityanak
semanticscholar   +2 more sources

On some identities of k-Jacobsthal-Lucas numbers

International Journal of Mathematical Analysis, 2014
In this paper we present the sequence of the k-Jacobsthal-Lucas numbers that generalizes the Jacobsthal-Lucas sequence introduced by Horadam in 1988. For this new sequence we establish an explicit formula for the term of order n, the well-known Binet’s ...
H. Campos, P. Catarino, A. P. Aires, P. Vasco, A. Borges   +4 more
semanticscholar   +2 more sources

On the k-Jacobsthal Lucas numbers of arithmetic indexes

International Journal of Contemporary Mathematical Sciences, 2016
In this paper, the k-Jacobsthal Lucas numbers of arithmetic indexes of the form an + r, where n is a natural number and r is less than a are investigated.
S. Uygun
semanticscholar   +2 more sources