Fibonacci series from power series

Kunle Adegoke
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 44—62
DOI: 10.7546/nntdm.2021.27.3.44-62
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Authors and affiliations

Kunle Adegoke
Department of Physics, Obafemi Awolowo University
220005 Ile-Ife, Nigeria

Abstract

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

Keywords

  • Fibonacci number
  • Lucas number
  • Summation identity
  • Series
  • Generating function
  • Gamma function
  • Digamma function
  • Trigonometric functions
  • Bernoulli number
  • Zeta function

2020 Mathematics Subject Classification

  • 11B39
  • 11B37

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Related papers

  1. Frontczak, R. (2020). Infinite series involving Fibonacci numbers and the Riemann zeta function. Notes on Number Theory and Discrete Mathematics, 26(2), 159–166.
  2. Adegoke, K., & Ghosh, S. (2021). Fibonacci-Zeta infinite series associated with the polygamma functions. Notes on Number Theory and Discrete Mathematics, 27(4), 95-103.

Cite this paper

Adegoke, K. (2021). Fibonacci series from power series. Notes on Number Theory and Discrete Mathematics, 27(3), 44-62, doi: 10.7546/nntdm.2021.27.3.44-62.

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