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

Dhairya Shah, Manoj Sahni, Ritu Sahni, Ernesto León-Castro and Maricruz Olazabal-Lugo
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Dhairya Shah: School of Liberal Studies, Pandit Deendayal Energy University, Gandhinagar 382426, India
Manoj Sahni: Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar 382426, India
Ritu Sahni: School of Liberal Studies, Pandit Deendayal Energy University, Gandhinagar 382426, India
Ernesto León-Castro: Faculty of Economics and Administrative Sciences, Universidad Católica de la Santísima Concepción, Concepción 4090541, Chile
Maricruz Olazabal-Lugo: Department of Economics and Administrative, Universidad Autónoma de Occidente, Culiacan 80139, Mexico

Mathematics, 2022, vol. 10, issue 9, 1-17

Abstract: In this part of a 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, polylogarithms 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 that 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 and showcase that these two theorems can provide hundreds of new results and thus can potentially create an entirely new field under the realm of number theory and analysis.

Keywords: ceiling function; floor function; Fibonacci number; generalised Dirichlet series; Lerch zeta function; Hurwitz zeta function; polylogarithm; Riemann zeta function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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