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
Download full paper: PDF, 185 Kb

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

  1. Abramowitz, M., & Stegun, I. A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New-York.
  2. Alzer, H., & Choi, J. (2017). The Riemann zeta function and classes of infinite series, Appl. Anal. Discrete Math., 11, 386–398.
  3. Alzer, H., & Choi, J. (2020). Four parametric linear Euler sums, J. Math. Anal. Appl. 484 (1), ID 123661. https://doi.org/10.1016/j.jmaa.2019.123661.
  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.
  6. Srivastava, H. M., & Choi, J. (2001). Series Associated with the Zeta and Related Functions, Dordrecht, Boston and London: Kluwer Academic Publishers.
  7. Srivastava, H. M., & Choi, J. (2012). Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York.
  8. Sloane, N. J. A. The On-Line Encyclopedia of Integer Sequences, Available online at: https://oeis.org.

Related papers

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.

Comments are closed.