Results 11 to 20 of about 472 (72)
Sequences of Non‐Gegenbauer‐Humbert Polynomials Meet the Generalized Gegenbauer‐Humbert Polynomials
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 Here, we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer‐Humbert polynomials. Many new and known transfer formulas between non‐Gegenbauer‐Humbert polynomials and generalized Gegenbauer‐Humbert polynomials are given.
Tian-Xiao He +4 more
wiley +1 more source
A note on modified third-order Jacobsthal numbers
Proyecciones (Antofagasta), 2020 Modified third-order Jacobsthal sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are also presented.
openaire +5 more sources
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
wiley +1 more source
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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On Hessenberg and pentadiagonal determinants related with Fibonacci and Fibonacci-like numbers [PDF]
, 2014 In this paper, we establish several new connections between the generalizations of Fibonacci and Lucas sequences and Hessenberg determinants. We also give an interesting conjecture related to the determinant of an infinite pentadiagonal matrix with the ...
Arı, Kamil, İpek, Ahmet
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Tribonacci and Tribonacci-Lucas Sedenions
, 2018 The sedenions form a 16-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tribonacci and Tribonacci-Lucas sedenions. Furthermore, we present some properties of these sedenions and derive relationships between them.Comment: 17 pages, 1 ...
Soykan, Yüksel
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Quantum Algorithms for Weighing Matrices and Quadratic Residues [PDF]
, 2000 In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms.
van Dam, Wim
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Sums of generalized third-order Jacobsthal numbers by matrix methods
Trends in Computational and Applied MathematicsIn this paper, we consider a certain third-order linear recurrence and then give generating matrices for the sums of positively and negatively subscripted terms of this recurrence.
G. Cerda-Morales
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Quadratic Approximation of Generalized Tribonacci Sequences
, 2018 In this paper, we give quadratic approximation of generalized Tribonacci sequence $\{V_{n}\}_{n\geq0}$ defined by Eq. (\ref{eq:7}) and use this result to give the matrix form of the $n$-th power of a companion matrix of $\{V_{n}\}_{n\geq0}$.
Cerda-Morales, Gamaliel
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On a Generalization for Tribonacci Quaternions
, 2017 Let $V_{n}$ denote the third order linear recursive sequence defined by the initial values $V_{0}$, $V_{1}$ and $V_{2}$ and the recursion $V_{n}=rV_{n-1}+sV_{n-2}+tV_{n-3}$ if $n\geq 3$, where $r$, $s$, and $t$ are real constants. The $\{V_{n}\}_{n\geq0}$
Cerda-Morales, Gamaliel
core +1 more source