Remarks on an Identity of Anastase and Díaz-Barrero

We extend an algebraic identity of Anastase and Díaz-Barrero (2022) and apply our results to deduce various formulas for sums and series involving (among others) Fibonacci and Lucas numbers, Bernoulli polynomials, and the Riemann zeta function.

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Bibliographic Details
Main Authors: Horst Alzer, Robert Frontczak
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Axioms
Subjects:
Online Access:https://www.mdpi.com/2075-1680/14/6/454
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author Horst Alzer
Robert Frontczak
author_facet Horst Alzer
Robert Frontczak
author_sort Horst Alzer
collection DOAJ
description We extend an algebraic identity of Anastase and Díaz-Barrero (2022) and apply our results to deduce various formulas for sums and series involving (among others) Fibonacci and Lucas numbers, Bernoulli polynomials, and the Riemann zeta function.
format Article
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institution Kabale University
issn 2075-1680
language English
publishDate 2025-06-01
publisher MDPI AG
record_format Article
series Axioms
spelling doaj-art-b4aa1129ce1a4465842847cbc77631222025-08-20T03:32:31ZengMDPI AGAxioms2075-16802025-06-0114645410.3390/axioms14060454Remarks on an Identity of Anastase and Díaz-BarreroHorst Alzer0Robert Frontczak1Morsbacher Straße 10, 51545 Waldbröl, GermanyAuf der Bloß 16, 72762 Reutlingen, GermanyWe extend an algebraic identity of Anastase and Díaz-Barrero (2022) and apply our results to deduce various formulas for sums and series involving (among others) Fibonacci and Lucas numbers, Bernoulli polynomials, and the Riemann zeta function.https://www.mdpi.com/2075-1680/14/6/454identityseriesharmonic numberpolylogarithmRiemann zeta functionFibonacci and Lucas numbers
spellingShingle Horst Alzer
Robert Frontczak
Remarks on an Identity of Anastase and Díaz-Barrero
Axioms
identity
series
harmonic number
polylogarithm
Riemann zeta function
Fibonacci and Lucas numbers
title Remarks on an Identity of Anastase and Díaz-Barrero
title_full Remarks on an Identity of Anastase and Díaz-Barrero
title_fullStr Remarks on an Identity of Anastase and Díaz-Barrero
title_full_unstemmed Remarks on an Identity of Anastase and Díaz-Barrero
title_short Remarks on an Identity of Anastase and Díaz-Barrero
title_sort remarks on an identity of anastase and diaz barrero
topic identity
series
harmonic number
polylogarithm
Riemann zeta function
Fibonacci and Lucas numbers
url https://www.mdpi.com/2075-1680/14/6/454
work_keys_str_mv AT horstalzer remarksonanidentityofanastaseanddiazbarrero
AT robertfrontczak remarksonanidentityofanastaseanddiazbarrero