Some Families of Apéry-Like Fibonacci and Lucas Series
In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed out.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-07-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/14/1621 |
| _version_ | 1827687376078503936 |
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| author | Robert Frontczak Hari Mohan Srivastava Živorad Tomovski |
| author_facet | Robert Frontczak Hari Mohan Srivastava Živorad Tomovski |
| author_sort | Robert Frontczak |
| collection | DOAJ |
| description | In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed out. |
| first_indexed | 2024-03-10T09:33:34Z |
| format | Article |
| id | doaj.art-95b6085b904544fda5e802063ee7700a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:33:34Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-95b6085b904544fda5e802063ee7700a2023-11-22T04:19:40ZengMDPI AGMathematics2227-73902021-07-01914162110.3390/math9141621Some Families of Apéry-Like Fibonacci and Lucas SeriesRobert Frontczak0Hari Mohan Srivastava1Živorad Tomovski2Landesbank Baden-Württemberg (LBBW), D-70173 Stuttgart, GermanyDepartment of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, Faculty of Science, University of Ostrava, 70103 Ostrava, Czech RepublicIn this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed out.https://www.mdpi.com/2227-7390/9/14/1621Riemann Zeta functioncentral binomial coefficientCatalan numbersFibonacci numbersLucas numbersharmonic numbers |
| spellingShingle | Robert Frontczak Hari Mohan Srivastava Živorad Tomovski Some Families of Apéry-Like Fibonacci and Lucas Series Mathematics Riemann Zeta function central binomial coefficient Catalan numbers Fibonacci numbers Lucas numbers harmonic numbers |
| title | Some Families of Apéry-Like Fibonacci and Lucas Series |
| title_full | Some Families of Apéry-Like Fibonacci and Lucas Series |
| title_fullStr | Some Families of Apéry-Like Fibonacci and Lucas Series |
| title_full_unstemmed | Some Families of Apéry-Like Fibonacci and Lucas Series |
| title_short | Some Families of Apéry-Like Fibonacci and Lucas Series |
| title_sort | some families of apery like fibonacci and lucas series |
| topic | Riemann Zeta function central binomial coefficient Catalan numbers Fibonacci numbers Lucas numbers harmonic numbers |
| url | https://www.mdpi.com/2227-7390/9/14/1621 |
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