A generalization of André-Jeannin’s symmetric identity

In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers , defined by a three-term recurrence = with constant coefficients. In this paper, we extend this identity to sequences satisfying a three-term recurrence = + with arbitrary coefficients. Then...

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Bibliographic Details
Published in:Pure mathematics and applications Vol. 27; no. 1; pp. 98 - 118
Main Author: Munarini, Emanuele
Format: Journal Article
Language:English
Hungarian
Published: Firenze Sciendo 01.07.2018
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:
Chebyshev polynomials
combinatorial sums
Fibonacci numbers
Fibonacci polynomials
Jacobsthal numbers
Jacobsthal polynomials
Lucas numbers
Lucas polynomials
Morgan-Voyce polynomials
Pell numbers
Pell polynomials
Primary 05A19
Secondary 05A30, 11B65
sums of reciprocals
three-term recurrences
ISSN:1788-800X, 1788-800X
Online Access:Get full text
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Summary:In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers , defined by a three-term recurrence = with constant coefficients. In this paper, we extend this identity to sequences satisfying a three-term recurrence = + with arbitrary coefficients. Then, we specialize such an identity to several -polynomials of combinatorial interest, such as the -Fibonacci, -Lucas, -Pell, -Jacobsthal, -Chebyshev and -Morgan-Voyce polynomials.
Bibliography:ObjectType-Article-1
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ISSN:1788-800X
1788-800X
DOI:10.1515/puma-2015-0028