Some results on convolved (<i>p</i>,<i>q</i>)-Fibonacci polynomials

Wang, Weiping; Wang, Hui

doi:10.1080/10652469.2015.1007502

Cited by 18 publications

(7 citation statements)

References 15 publications

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“…Theorem 18 is a generalization of the derivative given by several authors [2,7,14,15,16,29] for some Fibonacci-type polynomials and some Lucas-type polynomials. Recall that from (3) and ( 4 Evaluating the derivative of Fibonacci polynomials and the derivative of Lucas polynomials at x = 1 and x = 2 we obtain numerical sequences that appear in Sloan [25].…”

Section: Derivatives Of Gfpmentioning

confidence: 85%

The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials

Flórez,

Higuita,

Ramírez

2018

Preprint

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A second order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Known examples of these type of sequences are: Fibonacci polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials.The resultant of two polynomials is the determinant of the Sylvester matrix and the discriminant of a polynomial p is the resultant of p and its derivative. We study the resultant, the discriminant, and the derivatives of Fibonacci-type polynomials and Lucastype polynomials as well combinations of those two types. As a corollary we give explicit formulas for the resultant, the discriminant, and the derivative for the known polynomials mentioned above.

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Section: Derivatives Of Gfpmentioning

confidence: 85%

The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials

Flórez,

Higuita,

Ramírez

2018

Preprint

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“…The Fibonacci and Lucas sequences of both polynomials and numbers are of great importance in a variety of topics, such as number theory, combinatorics, and numerical analysis. For these studies, we refer to [38][39][40][41]. Table 1 provides the general solutions of such famous differential equations briefly.…”

Section: Applicationsmentioning

confidence: 99%

Further study on the conformable fractional Gauss hypergeometric function

Abul-Ez¹,

Zayed²,

Youssef³

2020

Preprint

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This paper presents a somewhat exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric equation (CFGHE) about the fractional regular singular points x = 1 and x = ∞. Next, various generating functions of the CFGHF are established. We also develop some differential forms for the CFGHF. Subsequently, differential operators and the contiguous relations are reported. Furthermore, we introduce the conformable fractional integral representation and the fractional Laplace transform of CFGHF. As an application, and after making a suitable change of the independent variable, we provide general solutions of some known conformable fractional differential equations, which could be written by means of the CFGHF.

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“…Please see the papers [11][12][13] and Wang and Wang. 14, p. 341, Table 1 After Lee and Asci's definition, Wang and Wang 14 defined the convolved (p, q)-Fibonacci polynomials as follows:…”

Section: Introductionmentioning

confidence: 99%

Explicit, determinantal, recursive formulas, and generating functions of generalized Humbert–Hermite polynomials via generalized Fibonacci polynomials

Kızılateş

2023

Math Methods in App Sciences

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In this paper, using the Faà di Bruno formula and some properties of the Bell polynomials of the second kind, we obtain a new explicit formula for the generalized Humbert-Hermite polynomials. We provide determinantal representations for the ratio of two differentiable functions. We obtain a recursive relation for the generalized Humbert-Hermite polynomials. As a practice, we derive an alternative recursive relation for generalized Humbert-Hermite polynomials via the Hessenberg determinant. Finally, we derive several families of multilinear and multilateral generating functions for the generalized Humbert-Hermite-type polynomials and other polynomials which are mentioned in this paper. Our results also include many well-known polynomials in the literature.

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Some results on convolved (p,q)-Fibonacci polynomials

Cited by 18 publications

References 15 publications

The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials

The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials

Further study on the conformable fractional Gauss hypergeometric function

Explicit, determinantal, recursive formulas, and generating functions of generalized Humbert–Hermite polynomials via generalized Fibonacci polynomials

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