New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

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

doi:10.1007/s11139-015-9712-x

New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

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

Araştırma sonucu: Dergi katkısı › Makale › bilirkişi

22 Alıntılar (Scopus)

Özet

We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type ₂F₁. Consequently, we obtain some new expressions for the celebrated Fibonacci numbers and their derivative sequences. Moreover, we evaluate some definite integrals involving products of Fibonacci and Chebyshev polynomials.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	347-361
Sayfa sayısı	15
Dergi	Ramanujan Journal
Hacim	42
Basın numarası	2
DOI'lar	https://doi.org/10.1007/s11139-015-9712-x
Yayın durumu	Yayınlanan - 1 Şub 2017
Harici olarak yayınlandı	Evet

Belgeye Erişim

10.1007/s11139-015-9712-x

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Bundan alıntı yap

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title = "New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials",

abstract = "We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type 2F1. Consequently, we obtain some new expressions for the celebrated Fibonacci numbers and their derivative sequences. Moreover, we evaluate some definite integrals involving products of Fibonacci and Chebyshev polynomials.",

keywords = "Chebyshev polynomials, Connection coefficients, Fibonacci numbers, Fibonacci polynomials, Hypergeometric functions",

author = "Abd-Elhameed, {W. M.} and Youssri, {Y. H.} and Nermine El-Sissi and Mohammad Sadek",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media New York.",

year = "2017",

month = feb,

day = "1",

doi = "10.1007/s11139-015-9712-x",

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T1 - New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

AU - Abd-Elhameed, W. M.

AU - Youssri, Y. H.

AU - El-Sissi, Nermine

AU - Sadek, Mohammad

PY - 2017/2/1

Y1 - 2017/2/1

N2 - We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type 2F1. Consequently, we obtain some new expressions for the celebrated Fibonacci numbers and their derivative sequences. Moreover, we evaluate some definite integrals involving products of Fibonacci and Chebyshev polynomials.

AB - We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type 2F1. Consequently, we obtain some new expressions for the celebrated Fibonacci numbers and their derivative sequences. Moreover, we evaluate some definite integrals involving products of Fibonacci and Chebyshev polynomials.

KW - Chebyshev polynomials

KW - Connection coefficients

KW - Fibonacci numbers

KW - Fibonacci polynomials

KW - Hypergeometric functions

UR - http://www.scopus.com/inward/record.url?scp=84939242888&partnerID=8YFLogxK

U2 - 10.1007/s11139-015-9712-x

DO - 10.1007/s11139-015-9712-x

M3 - Article

AN - SCOPUS:84939242888

SN - 1382-4090

VL - 42

SP - 347

EP - 361

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 2

ER -

New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

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