Bivariate fibonacci like p–polynomials

Tuglu, Naim; Kocer, E. Gokcen; Stakhov, Alexey

doi:10.1016/j.amc.2011.05.022

Cited by 37 publications

(27 citation statements)

References 16 publications

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“…Number theoretic properties such as these obtained from Fibonacci numbers relevant to this paper have been studied by many authors [1,4,7,11,12,20,23,27,28]. Now we define the generalized Fibonacci-circulant-Hurwitz numbers and then, we obtain their miscellaneous properties using the generating matrix and the generating function of these numbers.…”

Section: Introductionmentioning

confidence: 99%

On the Generalized Fibonacci-circulant-Hurwitz numbers

Devecı¹,

Adıgüzel²,

Doğan³

2020

NNTDM

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The theory of Fibonacci-circulant numbers was introduced by Deveci et al. (see [5]). In this paper, we define the Fibonacci-circulant-Hurwitz sequence of the second kind by Hurwitz matrix of the generating function of the Fibonacci-circulant sequence of the second kind and give a fair generalization of the sequence defined, which we call the generalized Fibonacci-circulant-Hurwitz sequence. First, we derive relationships between the generalized Fibonacci-circulant-Hurwitz numbers and the generating matrices for these numbers. Also, we give miscellaneous properties of the generalized Fibonacci-circulant-Hurwitz numbers such as the Binet formula, the combinatorial, permanental, determinantal representations, the generating function, the exponential representation and the sums.

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Section: Introductionmentioning

confidence: 99%

On the Generalized Fibonacci-circulant-Hurwitz numbers

Devecı¹,

Adıgüzel²,

Doğan³

2020

NNTDM

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“…In [7], the authors study bivariate Fibonacci and Lucas polynomials sequences and give some properties of these sequences. In [3], by using different matrices new sum formulae for bivariate Pell and Pell Lucas polynomials are obtained.…”

Section: Introductionmentioning

confidence: 99%

Bivariate Jacobsthal and Jacobsthal Lucas polynomial sequences

Uygun¹

2020

J. Math. Computer Sci.

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“…where F 0 = 0, F 1 = 1, L 0 = 2 and L 1 = 1, respectively. Many authors have investigated these polynomials and their generalizations [4][5][6][7][8][9][10][11][12]. In [8], Kim et al consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them.…”

Section: Introductionmentioning

confidence: 99%

On the (p, q)–Chebyshev Polynomials and Related Polynomials

2019

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In this paper, we introduce ( p , q ) –Chebyshev polynomials of the first and second kind that reduces the ( p , q ) –Fibonacci and the ( p , q ) –Lucas polynomials. These polynomials have explicit forms and generating functions are given. Then, derivative properties between these first and second kind polynomials, determinant representations, multilateral and multilinear generating functions are derived.

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Bivariate fibonacci like p–polynomials

Cited by 37 publications

References 16 publications

On the Generalized Fibonacci-circulant-Hurwitz numbers

On the Generalized Fibonacci-circulant-Hurwitz numbers

Bivariate Jacobsthal and Jacobsthal Lucas polynomial sequences

On the (p, q)–Chebyshev Polynomials and Related Polynomials

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