Relating Certain Weighted Fibonacci Series to Bernoulli Polynomials
via the Polylogarithm Function
Department of Physics and Engineering Physics
Obafemi Awolowo University
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.
Full version: pdf,
(Concerned with sequences
Received September 26 2020; revised versions received January 24 2021; January 30 2021.
Published in Journal of Integer Sequences,
January 30 2021.
Journal of Integer Sequences home page