Infinite series involving Fibonacci numbers and the Riemann zeta function

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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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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  4. Frontczak, R. (2020). Problem B-1267, Elementary Problems and Solutions, Fibonacci Quart. 58 (2), (2020), 179.
  5. Frontczak, R. (2020). Problem H-xxx, Advanced Problems and Solutions, Fibonacci Quart. 58 (3), to appear.
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  8. 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.

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