On the combined Jacobsthal-Padovan generalized quaternions - Gurses, Nurten; Isbilir, Zehra (TBILISI CENTRE MATH SCI, 2022)
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.
Keywords: the combined Jacobsthal-Padovan numbers; generalized quaternions; FIBONACCI NUMBERS; SEQUENCES; Mathematics