Results 1 to 10 of about 196 (109)
Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
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On Generalized Jacobsthal and Jacobsthal-Lucas polynomials [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's polynomials Jn(𝑥) and Jacobsthal-Lucas polynomials jn(𝑥).
Catarino Paula, Morgado Maria Luisa
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Communications in Algebra, 2019 AbstractIn this article, we find elements of the Lucas polynomials by using two matrices. We extend the study to the n-step Lucas polynomials.
Engin Özkan
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A Generalization of Lucas Polynomial Sequence
Discrete Applied Mathematics, 2009 The authors consider the problem of a generalization of Lucas polynomial sequence. They obtain a generalized Lucas polynomial sequence from the lattice paths for the Delannoy numbers by allowing weights on the steps \((1,0),(0,1)\) and \((1,1)\).
Gi-Sang Cheon, Hana Kim, Louis W Shapiro
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On Convolved Generalized Fibonacci and Lucas Polynomials [PDF]
Applied Mathematics and Computation, 2014 We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the convolved h(x)-Fibonacci polynomials form a family of Hessenberg matrices.
José L Ramirez
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Gaussian Pell-Lucas Polynomials
Communications in Mathematics and Applications, 2019 In this paper, we first define the Gaussian Pell-Lucas polynomial sequence. We then obtain Binet formula, generating function and determinantal representation of this sequence. Also, some properties of the Gaussian Pell-Lucas polynomials are investigated.
Tulay Yagmur
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The Sums of the Reciprocals of Fibonacci Polynomials and Lucas Polynomials [PDF]
Journal of Inequalities and Applications, 2012 AbstractIn this article, we consider infinite sums derived from the reciprocals of the Fibonacci polynomials and Lucas polynomials, and infinite sums derived from the reciprocals of the square of the Fibonacci polynomials and Lucas polynomials. Then applying the floor function to these sums, we obtain several new equalities involving the Fibonacci ...
Zhengang Wu, Wenpeng Zhang
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Fibonacci and Lucas Polynomials in n-gon
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each vertex. Also, we find the relation between the numbers with such vertices.
Kuloğlu Bahar +2 more
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Mathematics, 2018 In this paper, we derive Fourier series expansions for functions related to sums of finite products of Chebyshev polynomials of the first kind and of Lucas polynomials. From the Fourier series expansions, we are able to express those two kinds of sums of
Taekyun Kim, Dae San Kim, Gwan-Woo Jang
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Mathematics, 2022 The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients for a specific z.
Waleed Mohamed Abd-Elhameed +2 more
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