Some Classes of series involving the Riemann zeta function, Fibonacci numbers and the Lucas numbers

Abstract

The objective of this manuscript is to offer explicit expressions for diverse categories of infinite series incorporating the Fibonacci (Lucas) sequence and the Riemann zeta function. In demonstrating our findings, we will utilize conventional methodologies and integrate the Binet formulas pertinent to these sequences with generating functions that encompass the Riemann zeta function alongside established evaluations of certain series.