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

dc.creatorShah, Dhairya
dc.creatorSahni, Manoj
dc.creatorSahni, Ritu
dc.creatorLeón Castro, Ernesto
dc.creatorOlazabal Lugo, Maricruz
dc.date2022-10-13T14:19:58Z
dc.date2022-10-13T14:19:58Z
dc.date2022
dc.identifierShah, D., Sahni, M., Sahni, R., León-Castro, E., & Olazabal-Lugo, M. (2022). Series of floor and ceiling Functions—Part II: Infinite series. Mathematics, 10(9) doi:10.3390/math10091566
dc.identifier2227-7390
dc.identifierhttp://repositoriodigital.ucsc.cl/handle/25022009/2963
dc.descriptionArtículo de publicación SCOPUS - WOS
dc.descriptionIn 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.
dc.languageen
dc.publisherMathematics
dc.sourcefile:///D:/Downloads/mathematics-10-01566.pdf
dc.subjectCeiling function
dc.subjectFloor function
dc.subjectFibonacci number
dc.subjectGeneralised Dirichlet series
dc.subjectLerch zeta function
dc.subjectHurwitz zeta function
dc.subjectpolylogarithm
dc.subjectRiemann zeta function
dc.titleSeries of Floor and Ceiling Functions-Part II: Infinite Series
dc.typeArticle


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