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    On the combined Jacobsthal-Padovan generalized quaternions
    (Tbilisi Centre Math Sci, 2022) Gürses, Nurten; İşbilir, Zehra
    In this article, we examine the combined Jacobsthal-Padovan (CJP) generalized quaternions with four special cases: Jacobsthal-Padovan, Jacobsthal-Perrin, adjusted Jacobsthal-Padovan and modified Jacobsthal-Padovan generalized quaternions. Then, recurrence relation, generating function, Binet-like formula and exponential generating function of these quaternions are examined. In addition to this, some new properties, special determinant equations, matrix formulas and summation formulas are discussed.
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    Padovan, Perrin and Pell-Padovan Dual Quaternions
    (2023) İşbilir, Zehra; Gürses, Nurten
    In this present study, we intend to determine the Padovan, Perrin and Pell-Padovan dual quaternions with nonnegative and negative subscripts. In line with this purpose, we construct some new properties such as; special determinant equalities, new recurrence relations, matrix formulas, Binet-like formulas, generating functions, exponential generating functions, summation formulas, and binomial properties for these special dual quaternions.