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  4. Series of floor and ceiling functions—Part II: Infinite series
 
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Series of floor and ceiling functions—Part II: Infinite series
Dr. León-Castro, Ernesto 
Facultad de Ciencias Económicas y Administrativas 
Shah, Dhairya
Sahni, Manoj
Sahni, Ritu
Olazabal-Lugo, Maricruz
10.3390/math10091566
MDPI
2022
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.
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Series of floor and ceiling functions—Part II. Infinite series.pdf

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Checksum
Ceiling function
Floor function
Fibonacci number
Generalised Dirichlet series
Lerch zeta function
Hurwitz zeta function
Polylogarithm
Riemann zeta function
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