ON GENERALIZED (k, r) – GAUSS PELL NUMBERS

Kuloğlu, Bahar; Özkan, Engi̇n

doi:10.46939/j.sci.arts-21.3-a02

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2022

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Cited by 3 publications

(2 citation statements)

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“…One of these generalizations is Pell numbers. There are also many studies with Pell numbers [3,4,11,17]. This study is about Pell numbers and Eisenstein series and a similar procedure is used in [12].…”

Section: Introductionmentioning

confidence: 99%

On the Pell-Einstein series of power m

et al. 2022

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Section: Introductionmentioning

confidence: 99%

On the Pell-Einstein series of power m

et al. 2022

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“…Gaussian Fibonacci and Gaussian Lucas numbers and their polynomials are widely studied by many researchers [4,5,9,13]. These numbers are defined by the following recurrences [4]:…”

Section: Introductionmentioning

confidence: 99%

On the bicomplex Gaussian Fibonacci and Gaussian Lucas numbers

Özkan

Kuloğlu

2022

ACUTM

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We give the bicomplex Gaussian Fibonacci and the bicomplex Gaussian Lucas numbers and establish the generating functions and Binet’s formulas related to these numbers. Also, we present the summation formula, matrix representation and Honsberger identity and their relationship between these numbers. Finally, we show the relationships among the bicomplex Gaussian Fibonacci, the bicomplex Gaussian Lucas, Gaussian Fibonacci, Gaussian Lucas and Fibonacci numbers.

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d-Gaussian Pell polynomials and their matrix representation

Özkan

Uysal

2022

Discrete Math. Algorithm. Appl.

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We introduce a new generalization of Gaussian Pell polynomials. We call it [Formula: see text]-Gaussian Pell polynomials. Then we present the sum, generating functions and Binet formulas of these polynomials. We give the matrix representation of [Formula: see text]-Gaussian Pell polynomials. We introduce the matrix as binary representations according to the Riordan matrix representation. Using the Riordan method, we obtain the factorizations of the Pascal matrix involving the polynomial. In addition, we present the inverse of matrices of the polynomial.

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ON GENERALIZED (k, r) – GAUSS PELL NUMBERS

Cited by 3 publications

References 14 publications

On the Pell-Einstein series of power m

On the Pell-Einstein series of power m

On the bicomplex Gaussian Fibonacci and Gaussian Lucas numbers

d-Gaussian Pell polynomials and their matrix representation

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