Robert Frontczak

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 2, Pages 159—166

DOI: 10.7546/nntdm.2020.26.2.159-166

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## Details

### Authors and affiliations

Robert Frontczak

*Landesbank Baden-Württemberg
Am Hauptbahnhof 2, 70173 Stuttgart, Germany
*

### Abstract

Two new closed forms for infinite series involving Fibonacci numbers and the Riemann zeta function are derived using standard methods from complex analysis. Also, expressions for the companion series with Lucas numbers are presented.

### Keywords

- Fibonacci number
- Riemann zeta function
- Generating function

### 2010 Mathematics Subject Classification

- 11B37

11B39

40C15

### References

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- Frontczak, R. (2020). Problem B-1267, Elementary Problems and Solutions, Fibonacci Quart. 58 (2), (2020), 179.
- Frontczak, R. (2020). Problem H-xxx, Advanced Problems and Solutions, Fibonacci Quart. 58 (3), to appear.
- Srivastava, H. M., & Choi, J. (2001). Series Associated with the Zeta and Related Functions, Dordrecht, Boston and London: Kluwer Academic Publishers.
- Srivastava, H. M., & Choi, J. (2012). Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York.
- Sloane, N. J. A. The On-Line Encyclopedia of Integer Sequences, Available online at: https://oeis.org.

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## Cite this paper

Frontczak, R. (2020). Infinite series involving Fibonacci numbers and the Riemann zeta function. Notes on Number Theory and Discrete Mathematics, 26 (2), 159-166, doi: 10.7546/nntdm.2020.26.2.159-166.