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

Mathematics

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

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.

Original language	English
Pages (from-to)	347-361
Number of pages	15
Journal	Ramanujan Journal
Volume	42
Issue number	2
DOIs	https://doi.org/10.1007/s11139-015-9712-x
Publication status	Published - 1 Feb 2017

Keywords

Chebyshev polynomials
Connection coefficients
Fibonacci numbers
Fibonacci polynomials
Hypergeometric functions

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10.1007/s11139-015-9712-x

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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.",

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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

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New hypergeometric connection formulae between Fibonacci and Chebyshev polynomials

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