Series involving Dirichlet Eta function

Abstract

In this article, we obtain an integral representation for a remainder sum of the Dirichlet Eta function. We then obtain numerous generating functions and series concerning the usage of the obtained integral representation. Alternating Fibonacci sum of the partial sum of the Dirichlet Eta function has been obtained, as well as the squared version Fibonacci series concerning the sum. A generalized representation of the product of polynomials concerning the partial sum of the Dirichlet Eta function has been obtained. Numerous examples have been provided to showcase the derived results.