Journal of Integer Sequences, Vol. 24 (2021), Article 21.9.1

Series Involving Euler's Eta (or Dirichlet Eta) Function

Khristo Boyadzhiev
Department of Mathematics and Statistics
Ohio Northern University
Ada, OH 45810

Robert Frontczak
Landesbank Baden-Württemberg (LBBW)
Am Hauptbahnhof 2
70173 Stuttgart


In this article, we evaluate in closed form a number of series involving values of the Dirichlet eta function, and also Fibonacci and Lucas numbers. We also introduce a special constant representing the values of several such series.

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(Concerned with sequences A000032 A000045 A001008 A002805 A131688.)

Received May 14 2021; revised versions received May 16 2021; September 21 2021; September 26 2021. Published in Journal of Integer Sequences, September 29 2021.

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