A new family of k- Gaussian Fibonacci numbers

Taş, Sait

doi:10.25092/baunfbed.542440

Cited by 3 publications

(1 citation statement)

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“…numbers and their polynomials. A new family of k-Gaussian Fibonacci numbers is given by Taş [13] and a new family of Gaussian k-Fibonacci polynomials are defined by Taştan and Özkan [14]. Moreover they [10,11] presented a new families of Gaussian k-Jacobsthal numbers, Gaussian k-Jacobsthal-Lucas numbers and their polynomials and a new family of Gaussian k-Lucas numbers and their polynomials.…”

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confidence: 99%

On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials

Özimamoğlu

Kaya

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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In this paper, we generalize the known Gaussian Pell-Lucas numbers, and call such numbers as the generalized Gaussian k-Pell-Lucas numbers. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas numbers and the known Gaussian Pell-Lucas numbers. We generalize the known Gaussian Pell-Lucas polynomials, and call such polynomials as the generalized Gaussian k-Pell-Lucas polynomials. We obtain relations between the family of the generalized Gaussian k-Pell-Lucas polynomials and the known Gaussian Pell-Lucas polynomials. In addition, we present the new generalizations of these numbers and polynomials in matrix form. Then, we get Cassini’s identities for these numbers and polynomials.

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Section: Introductionmentioning

confidence: 99%

On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials

Özimamoğlu

Kaya

2023

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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ON GENERALIZED (k, r) – GAUSS PELL NUMBERS

Kuloğlu

Özkan

2021

J. Sci. Arts

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The complex-type Fibonacci p-Sequences

Devecı

Shannon

Karaduman

2022

AUCMCS

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In this paper, we define a new sequence which is called the complex-type Fibonacci p-sequence and we obtain the generating matrix of this complex-type Fibonacci p-sequence. We also derive the determinantal and the permanental representations. Then, using the roots of the characteristic polynomial of the complex-type Fibonacci p-sequence, we produce the Binet formula for this defined sequence. In addition, we give the combinatorial representations, the generating function, the exponential representation and the sums of the complex-type Fibonacci p-numbers.

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A new family of k- Gaussian Fibonacci numbers

Abstract: In this manuscript, a new family of ݇ − Gaussian Fibonacci numbers has been identified and some relationships between this family and known Gaussian Fibonacci numbers have been found. Also, I the generating functions of this family for ݇ = 2 has been obtained.

Cited by 3 publications

References 15 publications

On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials

On a new family of the generalized Gaussian k-Pell-Lucas numbers and their polynomials

ON GENERALIZED (k, r) – GAUSS PELL NUMBERS

The complex-type Fibonacci p-Sequences

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