On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications

Özkan, Engi̇n; Taştan, Merve

doi:10.1080/00927872.2019.1670193

Cited by 27 publications

(11 citation statements)

References 7 publications

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“…There is an extensive work in the literature concerning Fibonacci-type sequences and their applications in modern science (see e.g. [10,11,12] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Catalan transform of the k-Pell, k-Pell–Lucas and modified k-Pell sequence

Taştan¹,

Özkan²

2021

NNTDM

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In this study, we present the Catalan transforms of the k-Pell sequence, the k-Pell–Lucas sequence and the Modified k-Pell sequence and examine the properties of the sequences. Then we apply the Hankel transform to the Catalan transforms of the k-Pell sequence, the Catalan transform of the k-Pell–Lucas sequence and the Catalan transform of the Modified k-Pell sequence. Also, we obtain the generating functions of the Catalan transform of the k-Pell sequence, k-Pell–Lucas sequence and Modified k-Pell sequence. Furthermore, we acquire an interesting characteristic related to the determinant of the Hankel transform of the sequences.

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“…There is an extensive work in the literature concerning Fibonacci-type sequences and their applications in modern science (see e.g. [10,11,12] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Catalan transform of the k-Pell, k-Pell–Lucas and modified k-Pell sequence

Taştan¹,

Özkan²

2021

NNTDM

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“…Fibonacci number sequences have attractive properties and many applications in various branches of mathematics [3,5,14,21]. Historically too there have been different approaches to defining Fibonacci and Lucas polynomials [7,9,11,13,20].…”

Section: Introductionmentioning

confidence: 99%

The generalized k-Fibonacci polynomials and generalized k-Lucas polynomials

Taştan¹,

Özkan²,

Shannon³

2021

NNTDM

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In this paper, we define new families of Generalized Fibonacci polynomials and Generalized Lucas polynomials and develop some elegant properties of these families. We also find the relationships between the family of the generalized k-Fibonacci polynomials and the known generalized Fibonacci polynomials. Furthermore, we find new generalizations of these families and the polynomials in matrix representation. Then we establish Cassini’s Identities for the families and their polynomials. Finally, we suggest avenues for further research.

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“…We see some generalizations of Pell numbers in [11][12][13][14][15][16]. Also, we see some works on generalized Gauss numbers in [17][18][19]. In [18], Özkan and Taştan presented Gauss Fibonacci polynomials and Gauss Lucas polynomials and proved some theorems related to these polynomials.…”

Section: Introductionmentioning

confidence: 99%