New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

Abd-Elhameed, W. M.; Youssri, Y. H.; El-Sissi, Nermine; Sadek, Mohammad

doi:10.1007/s11139-015-9712-x

Cited by 22 publications

(13 citation statements)

References 21 publications

(28 reference statements)

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“…Remark 3. The two relations in (32) and (33) are in agreement with those recently developed in [13].…”

Section: Connection Formulae Between Two Different Generalized Polyno...supporting

confidence: 90%

“…Due to this importance, the connection problems between various polynomials have been investigated by many authors. In this regard, Abd-Elhameed et al in [13] solved the connection problems between Fibonacci polynomials and Chebyshev polynomials of first and second kinds. Some other studies concerning connection problems can be found in [14,15].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Novel Results of Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

Abd-Elhameed¹,

Zeyada²,

Philippou³

2020

Preprint

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This paper is concerned with developing some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. All the connection coefficients involve hypergeometric functions of the type 2 F 1 (z), for certain z. Several new connection formulae between some famous polynomials such as Fibonacci, Lucas, Pell, Fermat, Pell-Lucas, and Fermat-Lucas polynomials are deduced as special cases of the derived connection formulae. Some of the introduced formulae generalize some of those existing in the literature. As two applications of the derived connection formulae, some new formulae linking some celebrated numbers are given and also some newly closed formulae of certain definite weighted integrals are deduced. Based on using the two generalized classes of Fibonacci and Lucas polynomials, some new reduction formulae of certain odd and even radicals are developed.

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“…Remark 3. The two relations in (32) and (33) are in agreement with those recently developed in [13].…”

Section: Connection Formulae Between Two Different Generalized Polyno...supporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Novel Results of Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

Abd-Elhameed¹,

Zeyada²,

Philippou³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Some studies were devoted to solving these problems via different approaches. For some articles interested in investigating these problems, one can be referred for example to [20,21].…”

Section: Introductionmentioning

confidence: 99%

“…Several algorithms were described to solve the connection and linearization problems. In most cases, the connection and linearization coefficients are expressed in terms of hypergeometric functions of certain arguments; see, for example [20,[22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas

Abd-Elhameed

Youssri

2021

Adv Differ Equ

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The principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The connection coefficients are expressed in terms of terminating hypergeometric functions of certain arguments; however, they can be reduced in some cases. New moment formulas of the sixth-kind Chebyshev polynomials are also established, and in virtue of such formulas, linearization formulas of these polynomials are developed.

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“…In fact, the literature on this subject is vast and a wide variety of methods have been developed using several techniques. Here, we refer mainly to the following references [1,2,3,8,11,24,30,31,49,50,56]. Zeros of orthogonal polynomials is another widely discussed subject due to its applications in several problems of applied sciences [54] and their crucial role in quadrature formulas [22].…”

Section: Introductionmentioning

confidence: 99%

On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind

Rocha

2019

Journal of Difference Equations and Applications

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Orthogonal polynomials satisfy a recurrence relation of order two, where appear two coefficients. If we modify one of these coefficients at a certain order, we obtain a perturbed orthogonal sequence. In this work we consider in this way some perturbed of Chebyshev polynomials of second kind and we deal with the problem of finding the connection coefficients that allow to write the perturbed sequence in terms of the original one and in terms of the canonical basis. From the connection relations obtained and from two other relations, we deduce some results about zeros and interception points of these perturbed polynomials. All the work is valid for arbitrary order of perturbation.

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New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

Cited by 22 publications

References 21 publications

Novel Results of Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

Novel Results of Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas

On connection coefficients of some perturbed of arbitrary order of the Chebyshev polynomials of second kind

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