Results 131 to 140 of about 1,148,545 (158)

Generalization of Gaussian Mersenne numbers and their new families

Mathematics and Computer Science
In this article, we present the generalized Gaussian Mersenne numbers with arbitrary initial values and discuss two particular cases, namely, Gaussian Mersenne and Gaussian Mersenne-Lucas numbers.
Munesh Kumari, K. Prasad, J. Tanti
semanticscholar   +1 more source

Leonardo Numbers and their Bicomplex Extension

Nepal Journal of Mathematical Sciences
This paper introduces a new type of Leonardo numbers, referred to as bicomplex Leonardoi numbers. Also, some important relations, including the generating function, Binet's formula, D'Ocagne's identity, Cassini’s identity, and Catalan’s identity ...
M. Jaiswal, N. Pahari, Purushottam Parajuli   +2 more
semanticscholar   +1 more source

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 Dual Hyperbolic Generalised Leonardo Numbers

Asian Research Journal of Mathematics
In this study, we present a comprehensive formalization of dual hyperbolic generalized Leonardo numbers, systematically examining their structural properties and mathematical significance.
C. M. Dikmen
semanticscholar   +1 more source

The Binet Formulas for the Pell and Pell-Lucas p-Numbers.

Ars Comb., 2007
In this paper, we define the Pell and Pell-Lucas p-numbers and derive the analytical formulas for these numbers. These formulas are similar to Bin et's formula for the classical Pell numbers.
Kocer, E. Gokcen, Tuglu, Naim
openaire   +2 more sources

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

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, P. Catarino
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

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