Journal of Integer Sequences, Vol. 24 (2021), Article 21.2.6

Relating Certain Weighted Fibonacci Series to Bernoulli Polynomials via the Polylogarithm Function


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

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.


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(Concerned with sequences A000032 A000045.)


Received September 26 2020; revised versions received January 24 2021; January 30 2021. Published in Journal of Integer Sequences, January 30 2021.


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