Results 11 to 20 of about 81 (66)
On third-order Jacobsthal numbers and their bihyperbolic generalizations
Annales Universitatis Mariae Curie-Sklodowska, sectio A – MathematicaIn this paper, we introduce bihyperbolic third-order Jacobsthal and third-order Jacobsthal--Lucas numbers. In other words, bihyperbolic numbers whose coefficients are consecutive third-order Jacobsthal and third-order Jacobsthal--Lucas numbers. Furthermore, we study one parameter generalizations of bihyperbolic third-order Jacobsthal and third-order ...
Morales, Gamaliel
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A note on dual third-order Jacobsthal vectors [PDF]
, 2020 Third-order Jacobsthal quaternions are first defined by [5]. In this study, dual third-order Jacobsthal and dual third-order Jacobsthal–Lucas numbers are defined. Furthermore, we work on these dual numbers and we obtain the properties e.g.
Cerda-Morales, Gamaliel
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De Moivre-type Identities for the Jacobsthal Numbers
, 2021 The main aim of this study is to obtain De Moivre-type identities for Jacobsthal numbers. Also, this paper presents a method for constructing the second order Jacobsthal and Jacobsthal third-order numbers and the third-order Jacobsthal and Jacobsthal ...
Akbıyık, Mücahit +1 more
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Higher-Order Jacobsthal–Lucas Quaternions
, 2022 In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions.
Engin Özkan, Mine Uysal
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On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
International Journal of Mathematics and Mathematical Sciences, Volume 2009, Issue 1, 2009., 2009 Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer‐Humbert polynomials are also discussed.
Tian-Xiao He +2 more
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A note on binomial transform of the generalized fifth order Jacobsthal numbers
, 2022 In this paper, we define the binomial transform of the generalized fifth order Jacobsthal sequence and as special cases, the binomial transform of the fifth order Jacobsthal, fifth order Jacobsthal-Lucas, adjusted fifth order Jacobsthal and modified ...
Erkan Taşdemir +2 more
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Asymptotic behavior of a class of nonlinear difference equations
Discrete Dynamics in Nature and Society, Volume 2006, Issue 1, 2006., 2006 Motivated by some results of L. Berg (2002), in this paper we find the second member in the asymptotic development of some of the positive solutions of a class of difference equations of second and third orders. The main result in this paper partially solves an open problem by S.
Stevo Stevic
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, 2023 In this paper, we define and investigate the generalized Friedrich sequences and we deal with, in detail, two special cases, namely, Friedrich and Friedrich-Lucas sequences.
Yüksel Soykan
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Matrix Structure of Jacobsthal Numbers
, 2021 The main scenario of this paper is to introduce a new sequence of Jacobsthal type having a generalized order j. Some basic properties will be studied concerning it.
Abdul Hamid Ganie, Mashael M. AlBaidani
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Binomial Transforms of the Third-Order Jacobsthal and Modified Third-Order Jacobsthal Polynomials
Universal Journal of Mathematics and ApplicationsIn this study, we define the binomial transforms of third-order Jacobsthal and modified third-order Jacobsthal polynomials. Further, the generating functions, Binet formulas and summation of these binomial transforms are found by recurrence relations ...
Gamaliel Morales
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