Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers

Guo, Dongwei; Chu, Wenchang

doi:10.3390/math10152667

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…These linear recurrence sequences will in turn lead to the following general formulae (5,6) T α (z) = 1 2…”

Section: Introductionmentioning

confidence: 99%

Some Identities on Sums of Finite Products of the Pell, Fibonacci, and Chebyshev Polynomials

Kishore¹,

Verma²

2023

IJST

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Objectives: This study will introduce some new identities for sums of finite products of the Pell, Fibonacci, and Chebyshev polynomials in terms of derivatives of Pell polynomials. Similar identities for Fibonacci and Lucas numbers will be deduced. Methods: Results are obtained by using differential calculus, combinatory computations, and elementary algebraic computations. Findings: In terms of derivatives of Pell polynomials, identities on sums of finite products of the Fibonacci numbers, Lucas numbers, Pell and Fibonacci polynomials, and Chebyshev polynomials of third and fourth kinds are obtained. Novelty: Existing research has identified identities on sums of finite products of the Fibonacci numbers, Lucas numbers, Pell and Fibonacci polynomials, and Chebyshev polynomials of the third and fourth kinds in terms of derivatives of Fibonacci polynomials or Chebyshev polynomials; identities on sums of finite products in terms of Pell polynomials, however, have not been investigated, so identities primarily in terms of Pell polynomials are obtained.

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“…These linear recurrence sequences will in turn lead to the following general formulae (5,6) T α (z) = 1 2…”

Section: Introductionmentioning

confidence: 99%

Some Identities on Sums of Finite Products of the Pell, Fibonacci, and Chebyshev Polynomials

Kishore¹,

Verma²

2023

IJST

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“…These numbers are connected with complex valued fuctions, and they give a generalization of the Pell sequence and Fibonacci sequence. After this study, mathematicians worked on this issue in [5,6]. Then, generalized Fibonacci numbers and k-Fibonacci numbers were studied with matrices in [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Ordered Leonardo Quadruple Numbers

Nurkan

Güven

2023

Symmetry

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In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric properties of Fibonacci numbers are used in the proofs. We attain some well-known identities, the Binet formula, and a generating function for these numbers. Finally, we provide illustrations of the identities.

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Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers

Abstract: 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.

Cited by 2 publications

References 24 publications

Some Identities on Sums of Finite Products of the Pell, Fibonacci, and Chebyshev Polynomials

Some Identities on Sums of Finite Products of the Pell, Fibonacci, and Chebyshev Polynomials

Ordered Leonardo Quadruple Numbers

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