On the 3-parameter generalized quaternions with generalized tribonacci numbers components

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dc.contributor.authorIsbilir, Zehra
dc.contributor.authorGurses, Nurten
dc.contributor.authorTosun, Murat
dc.date.accessioned2025-10-11T20:47:53Z
dc.date.available2025-10-11T20:47:53Z
dc.date.issued2025
dc.departmentDüzce Üniversitesien_US
dc.description.abstractIn this paper, we aim to combine 3-parameter generalized quaternions (shortly 3PGQs), which are a general form of the quaternion algebra according to 3-parameters, and generalized Tribonacci number (shortly GTNs), which are also quite a big special number family for third-order recurrence sequences and most general form of all of the third-order recurrence sequences. Namely, we investigate a special new number system called 3-parameter generalized quaternions with generalized Tribonacci numbers components (shortly 3PGQs with GTN components) with both nonnegative and negative subscripts and examine some special cases of them. Then, we construct a Maple code of this special number family. Moreover, we obtain some new and classical well-known equations such as; Binet formulas, generating function, exponential generating function, Poisson generating function, summation formulas, polar representation, and matrix equation. In addition to these, we give also determinant, characteristic polynomial, characteristic equation, eigenvalues, and eigenvectors concerning the matrix representation of 3PGQs with GTN components.en_US
dc.identifier.doi10.2298/FIL2509003I
dc.identifier.endpage3027en_US
dc.identifier.issn0354-5180
dc.identifier.issue9en_US
dc.identifier.scopus2-s2.0-105001134568en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage3003en_US
dc.identifier.urihttps://doi.org/10.2298/FIL2509003I
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21631
dc.identifier.volume39en_US
dc.identifier.wosWOS:001470414100013en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherUniv Nis, Fac Sci Mathen_US
dc.relation.ispartofFilomaten_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKA_WOS_20250911
dc.subject3-parameter generalized quaternionsen_US
dc.subjectgeneralized Tribonacci numbersen_US
dc.titleOn the 3-parameter generalized quaternions with generalized tribonacci numbers componentsen_US
dc.typeArticleen_US

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