Relating certain weighted Fibonacci series to Bernoulli polynomials via the polylogarithm function

2020/09/14 by Kunle Adegoke, Adegoke, Kunle
Mathematics · Physics and Astronomy · #11B37 #11B39 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B37 #msc:11B39

paper · pdf · doi:10.48550/arxiv.2009.11703

14 pages, no figures or tables

openalex publication_date 2020/09/14 · arxiv created 2020/09/26 · arxiv updated 2020/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that certain weighted Fibonacci and Lucas series can always be expressed as linear combinations of polylogarithms. In some special cases we evaluate the series in terms of Bernoulli polynomials, making use of the connection between these polynomials and the polylogarithm.

Related

• More Fibonacci-Bernoulli relations with and without balancing polynomials
• Additional Fibonacci-Bernoulli relations
• Some power series extensions of Fibonacci and Lucas polynomials
• Remarkable relations between the central binomial series, Eulerian polynomials, and poly-Bernoulli numbers
• Polylogarithms, hyperfunctions and generalized Lipschitz summation formulae