Some new results for the ( p , q ) -Fibonacci and Lucas polynomials

Wang, Jingzhe

doi:10.1186/1687-1847-2014-64

Cited by 11 publications

(3 citation statements)

References 8 publications

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“…We can give some references on special cases of second-order linear recurrence sequences of polynomials and numbers. For example, see [1,2,3,4,5,6,7] for papers and [8,9,10,11,12,13,14] for books.…”

Section: Introduction: Horadam (Generalized Fibonacci) Polynomialsmentioning

confidence: 99%

Generalized Horadam-Leonardo Numbers and Polynomials

Soykan

2023

AJARR

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In this study, we define and investigate some linear third order polynomials called the generalized Horadam-Leonardo polynomials (with its two special cases, namely), (r, s)-Horadam-Leonardo and (r, s)-Horadam-Leonardo-Lucas polynomials. We give Binet’s formulas, generating functions, Simson formulas, and the sumformulas for these polynomial sequences. Also, we present some identities and matrices related to thesepolynomials. Furthermore, we present some special cases of generalized Horadam-Leonardo polynomials,namely, generalized Leonardo, generalized John, generalized Ernst, generalized Pisano, generalized Edouardand generalized Bigollo numbers.

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Section: Introduction: Horadam (Generalized Fibonacci) Polynomialsmentioning

confidence: 99%

Generalized Horadam-Leonardo Numbers and Polynomials

Soykan

2023

AJARR

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“…We choose to remark in passing that several authors (see, for example, [23] and [24]) studied the so-called .p; q/-Fibonacci and .p; q/-Lucas polynomials by introducing a seemingly redundant parameter p, since the so-called .p; q/-number OEn p;q is given (for 0 < q < p 5 1) by…”

Section: Introductionmentioning

confidence: 99%

Some results on the q-analogues of the incomplete Fibonacci and Lucas Polynomials

Srivástava¹,

Tuglu²,

Çetin³

2019

MMN

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In the present paper, we introduce new families of the q-Fibonacci and q-Lucas polynomials, which are represented here as the incomplete q-Fibonacci polynomials F k n .x; s; q/ and the incomplete q-Lucas polynomials L k n .x; s; q/, respectively. These polynomials provide the q-analogues of the incomplete Fibonacci and Lucas numbers. We give several properties and generating functions of each of these families q-polynomials. We also point out the fact that the results for the q-analogues which we consider in this article for 0 < q < 1 can easily be translated into the corresponding results for the .p; q/-analogues (with 0 < q < p 5 1) by applying some obvious parametric variations, the additional parameter p being redundant.

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“…properties and applications to almost every field. For some references on special cases of second-order linear recurrence sequences of polynomials and numbers, see for instance [4,5,6,14,18,19] for papers and [1,3,8,9,10,15,17] for books.…”

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confidence: 99%

Generalized Tribonacci Polynomials

Soykan

2023

EJMS

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In this paper, we investigate the generalized Tribonacci polynomials and we deal with, in detail, two special cases which we call them (r,s,t)-Tribonacci and (r,s,t)-Tribonacci-Lucas polynomials. We also introduce and investigate a new sequence and its two special cases namely the generalized co-Tribonacci, (r,s,t)-co-Tribonacci and (r,s,t)-co-Tribonacci-Lucas polynomials, respectively. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these polynomial sequences. Moreover, we give some identities and matrices related to these polynomials. Furthermore, we evaluate the infinite sums of special cases of (r,s,t)-Tribonacci and (r,s,t)-Tribonacci-Lucas polynomials.

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Some new results for the ( p , q ) -Fibonacci and Lucas polynomials

Cited by 11 publications

References 8 publications

Generalized Horadam-Leonardo Numbers and Polynomials

Generalized Horadam-Leonardo Numbers and Polynomials

Some results on the q-analogues of the incomplete Fibonacci and Lucas Polynomials

Generalized Tribonacci Polynomials

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