ARTICLE | doi:10.20944/preprints202204.0176.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: ceiling function; floor function; Fibonacci Number; Generalised Dirichlet series; Lerch - Zeta Function; Hurwitz - Zeta function; Polylogarithm; Riemann-Zeta function
Online: 19 April 2022 (06:03:59 CEST)
In this part of the series of two papers, we extend the theorems discussed in part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, Polylogarithm and Fibonacci numbers. In continuation, we obtain some zeros of the newly developed zeta functions and explain their behaviour using plots in complex plane. Furthermore, we provide particular cases for the theorems and corollaries which show that our results generalise the currently available functions and series such as the Riemann zeta function and the geometric series. Finally, we provide four miscellaneous examples to showcase the vast scope of the developed theorems.