Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Series of Floor and Ceiling Function—Part II: Infinite Series

Version 1 : Received: 16 April 2022 / Approved: 19 April 2022 / Online: 19 April 2022 (06:03:59 CEST)

A peer-reviewed article of this Preprint also exists.

Shah, D.; Sahni, M.; Sahni, R.; León-Castro, E.; Olazabal-Lugo, M. Series of Floor and Ceiling Functions—Part II: Infinite Series. Mathematics 2022, 10, 1566. Shah, D.; Sahni, M.; Sahni, R.; León-Castro, E.; Olazabal-Lugo, M. Series of Floor and Ceiling Functions—Part II: Infinite Series. Mathematics 2022, 10, 1566.

Journal reference: Mathematics 2022, 10, 1566
DOI: 10.3390/math10091566

Abstract

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.

Keywords

ceiling function; floor function; Fibonacci Number; Generalised Dirichlet series; Lerch - Zeta Function; Hurwitz - Zeta function; Polylogarithm; Riemann-Zeta function

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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