Numerical evaluation of special power series including the numbers of Lyndon words: an approach to interpolation functions for apostol-type numbers and polynomials

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dc.contributor.authorKüçükoğlu, İrem
dc.contributor.authorŞimşek, Yılmaz
dc.date.accessioned2021-02-19T21:16:40Z
dc.date.available2021-02-19T21:16:40Z
dc.date.issued2018
dc.departmentALKÜ
dc.descriptionKUCUKOGLU, IREM/0000-0001-9100-2252;
dc.description.abstractBecause the Lyndon words and their numbers have practical applications in many different disciplines such as mathematics, probability, statistics, computer programming, algorithms, etc., it is known that not only mathematicians but also statisticians, computer programmers, and other scientists have studied them using different methods. Contrary to other studies, in this paper we use methods associated with zeta-type functions, which interpolate the family of Apostol-type numbers and polynomials of order k. Therefore, the main purpose of this paper is not only to give a special power series including the numbers of Lyndon words and binomial coefficients but also to construct new computational algorithms in order to simulate these series by numerical evaluations and plots. By using these algorithms, we provide novel computational methods to the area of combinatorics on words including Lyndon words. We also define new functions related to these power series, Lyndon words counting numbers, and the Apostoltype numbers and polynomials. Furthermore, we present some illustrations and observations on approximations of functions by rational functions associated with Apostol-type numbers that can provide ideas on the reduction of the algorithmic complexity of these algorithms.
dc.description.sponsorshipScientific Research Project Administration of Akdeniz UniversityAkdeniz University [FBA-2018-3292]
dc.description.sponsorshipThe present paper was supported by Scientific Research Project Administration of Akdeniz University (with Project Number: FBA-2018-3292).
dc.identifier.doi10.1553/etna_vol50s98
dc.identifier.endpage108en_US
dc.identifier.issn1068-9613
dc.identifier.scopusqualityQ2
dc.identifier.startpage98en_US
dc.identifier.urihttps://doi.org/10.1553/etna_vol50s98
dc.identifier.urihttps://hdl.handle.net/20.500.12868/512
dc.identifier.volume50en_US
dc.identifier.wosWOS:000459296200007
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthor0-belirlenecek
dc.language.isoen
dc.publisherKent State University
dc.relation.ispartofElectronic Transactions On Numerical Analysis
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectLyndon words
dc.subjectspecial numbers and polynomials
dc.subjectApostol-type numbers and polynomials
dc.subjectarithmetical function
dc.subjectinterpolation function
dc.subjectzeta type function
dc.titleNumerical evaluation of special power series including the numbers of Lyndon words: an approach to interpolation functions for apostol-type numbers and polynomials
dc.typeArticle

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