On interpolation functions for the number of k-ary Lyndon words associated with the Apostol-Euler numbers and their applications

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dc.authoridKucukoglu, Irem/0000-0001-9100-2252
dc.authorwosidSIMSEK, YILMAZ/C-1654-2016
dc.authorwosidKucukoglu, Irem/L-9198-2018
dc.contributor.authorKüçükoğlu, İrem
dc.contributor.authorŞimşek, Yılmaz
dc.date.accessioned2024-08-20T20:29:20Z
dc.date.available2024-08-20T20:29:20Z
dc.date.issued2019
dc.departmentAntalya Belek Üniversitesien_US
dc.description.abstractThe aim of this paper is to construct interpolation functions for the numbers of the k-ary Lyndon words which count n digit primitive necklace class representative on the set of the k-letter alphabet. By using the unified zeta-type function and the unification of the Apostol-type numbers which are defined by Ozden et al. (Comput Math Appl 60:2779-2787, 2010), we give an alternating series for the numbers of the k-ary Lyndon words, in terms of the Apostol-Euler numbers and Frobenius-Euler numbers. We investigate various properties of these functions. Furthermore, applying higher order derivative operator to the interpolation functions for the Lyndon words, we derive ODEs including Stirling-type numbers, the Apostol-Euler numbers, the unified zeta-type functions and also combinatorial sums. By using recurrence relation of the Apostol-Euler numbers, we give computation algorithms for computing not only the Apostol-Euler numbers but also the interpolation functions of the numbers . We also give some remarks, observations and computations for sums of infinite series including these interpolation functions.en_US
dc.description.sponsorshipScientific Research Project Administration of Akdeniz University [FDK-2017-2375]en_US
dc.description.sponsorshipThe present paper was supported by Scientific Research Project Administration of Akdeniz University (with Project Number: FDK-2017-2375).en_US
dc.identifier.doi10.1007/s13398-017-0471-y
dc.identifier.endpage297en_US
dc.identifier.issn1578-7303
dc.identifier.issn1579-1505
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-85060501057en_US
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage281en_US
dc.identifier.urihttps://doi.org/10.1007/s13398-017-0471-y
dc.identifier.urihttps://hdl.handle.net/20.500.14591/103
dc.identifier.volume113en_US
dc.identifier.wosWOS:000456622200022en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSPRINGER-VERLAG ITALIA SRLen_US
dc.relation.ispartofRevista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicasen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectLyndon wordsen_US
dc.subjectGenerating functionsen_US
dc.subjectSpecial numbersen_US
dc.subjectSpecial polynomialsen_US
dc.subjectDifferential operatoren_US
dc.subjectAlgorithmen_US
dc.subjectStirling numbers of the first kinden_US
dc.subjectApostol-Euler numbers and polynomialsen_US
dc.subjectFrobenius-Euler numbers and polynomialsen_US
dc.subjectArithmetical functionsen_US
dc.titleOn interpolation functions for the number of k-ary Lyndon words associated with the Apostol-Euler numbers and their applicationsen_US
dc.typeArticleen_US

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