Fibonacci-Zeta infinite series associated with the polygamma functions

Kunle Adegoke and Sourangshu Ghosh
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 4, Pages 95–103
DOI: 10.7546/nntdm.2021.27.4.95-103
Full paper (PDF, 172 Kb)

Details

Authors and affiliations

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

Sourangshu Ghosh
Department of Civil Engineering
Indian Institute of Technology, Kharagpur, India

Abstract

We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.

Keywords

• Fibonacci numbers and Lucas numbers
• Summation identity
• Series
• Digamma function
• Polygamma function
• Zeta function

2020 Mathematics Subject Classification

• Primary: 11B39
• Secondary:
  • 33B15
  • 11B37

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