Results 41 to 50 of about 14,002 (132)
Symmetric and generating functions of generalized (p,q)-numbers
Kuwait Journal of Science, 2021 In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions of (p,q)-Fibonacci numbers, (p,q)-Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q ...
Nabiha Saba +2 more
doaj +1 more source
Horadam Polynomials and a Class of Biunivalent Functions Defined by Ruscheweyh Operator
International Journal of Mathematics and Mathematical Sciences, Volume 2023, Issue 1, 2023., 2023 In this paper, we introduce and investigate a class of biunivalent functions, denoted by Hn,r,α, that depends on the Ruscheweyh operator and defined by means of Horadam polynomials. For functions in this class, we derive the estimations for the initial Taylor–Maclaurin coefficients |a2| and |a3|.
Waleed Al-Rawashdeh, Teodor Bulboaca
wiley +1 more source
On New Polynomial Sequences Constructed to Each Vertex in an n‐Gon
Discrete Dynamics in Nature and Society, Volume 2022, Issue 1, 2022., 2022 In this work, we bring to light the properties of newly formed polynomial sequences at each vertex of Pell polynomial sequences placed clockwise at each vertex in the n‐gon. We compute the relation among the polynomials with such vertices. Moreover, in an n‐gon, we generate a recurrence relation for a sequence giving the mth term formed at the kth ...
Abdul Hamid Ganie +4 more
wiley +1 more source
Matrix Structure of Jacobsthal Numbers
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 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. Also, we will establish the generalized Binet formula.
Abdul Hamid Ganie +2 more
wiley +1 more source
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 We use a new method of matrix decomposition for r‐circulant matrix to get the determinants of An = Circr(F1, F2, …, Fn) and Bn = Circr(L1, L2, …, Ln), where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived.
Jiangming Ma +3 more
wiley +1 more source
Catalan Transform of k‐Balancing Sequences
International Journal of Mathematics and Mathematical Sciences, Volume 2021, Issue 1, 2021., 2021 In this work, the Catalan transformation (CT) of k‐balancing sequences, Bk,nn≥0, is introduced. Furthermore, the obtained Catalan transformation CBk,nn≥0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k‐balancing sequences, Bk,nn≥0, which is an n × 1 matrix.
Asim Patra +2 more
wiley +1 more source
On Some Properties of Bihyperbolic Numbers of The Lucas Type
Communications in Advanced Mathematical Sciences, 2023 To date, many authors in the literature have worked on special arrays in various computational systems. In this article, Lucas type bihyperbolic numbers were defined and their algebraic properties were examined. Bihyperbolic Lucas numbers were studied by
Fügen Torunbalcı Aydın
doaj +1 more source
Some identities for generalized Fibonacci and Lucas numbers
AKCE International Journal of Graphs and Combinatorics, 2020 In this paper we study one parameter generalization of the Fibonacci numbers, Lucas numbers which generalizes the Jacobsthal numbers, Jacobsthal–Lucas numbers simultaneously. We present some their properties and interpretations also in graphs.
Anetta Szynal-Liana +2 more
doaj +1 more source
On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions [PDF]
, 2022 summary:We study generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. We present some properties of these quaternions and the relations between the generalized commutative Jacobsthal quaternions and ...
Bród, Dorota +2 more
core +1 more source
Some Special Identities for Jacobsthal and Jacobsthal-Lucas Generalized Octonions [PDF]
, 2022 Summary: We study on Jacobsthal and Jacobsthal-Lucas generalized octonions over the algebra \(\mathbb{O}(a, b, c)\) where \(a\), \(b\) and \(c\) are real numbers. We present Binet formulas for these types of octonions.
Mert, Tuğba +3 more
core +1 more source