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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| Format: | Article |
| Language: | English |
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MDPI AG
2025-06-01
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| Series: | Axioms |
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| 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 |
| id | doaj-art-b4aa1129ce1a4465842847cbc7763122 |
| 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 |