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A NEW FAMILIES OF GAUSS k-JACOBSTHAL NUMBERS AND GAUSS k-JACOBSTHAL-LUCAS NUMBERS AND THEIR POLYNOMIALSOzkan, EnginTastan, MerveGauss Jacobsthal polynomialsGauss Jacobsthal-Lucas polynomialsCassini's identitygenerating functionFIBONACCIMultidisciplinary SciencesScience & Technology - Other TopicsIn this paper, we define the new families of Gauss k-Jacobsthal numbers and Gauss k-Jacobsthal-Lucas numbers. We obtain some exciting properties of the families. We give the relationships between the family of the Gauss k-Jacobsthal numbers and the known Gauss Jacobsthal numbers, the family of the Gauss k-Jacobsthal-Lucas numbers and the known Gauss Jacobsthal-Lucas numbers. We also define the generalized polynomials for these numbers. Further, we obtain some interesting properties of the polynomials. In addition, we give the relationships between the generalized Gauss k-Jacobsthal polynomials and the known Gauss Jacobsthal polynomials, the generalized Gauss k-Jacobsthal-Lucas polynomials and the known Gauss Jacobsthal-Lucas polynomials. Furthermore, we find the new generalizations of these families and the polynomials in matrix representation. Then we prove Cassini's Identities for the families and their polynomials.EDITURA BIBLIOTHECA-BIBLIOTHECA PUBL HOUSE2020Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/16636https://doi.org/10.46939/j.sci.arts-20.4-a101844-9581enJOURNAL OF SCIENCE AND ARTSinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/16636