In this paper, we first define the Gaussian modified Pell sequence, for n ≥ 2, by the relation = 2 −1 + −2 with initial conditions 0 = 1 ─ i and 1 = 1 + i. Then we give the definition of the Gaussian modified Pell polynomial sequence, for n ≥ 2, by the relation ( ) = 2 −1 ( ) + −2 ( ) with initial conditions 0 ( ) = 1─ xi and 1 ( ) = x + i. We give Binet's formulas, generating functions and summation formulas of these sequences. We also obtain some well-known identities such as Catalan's identities, Cassini's identities and d'Ocagne's identities involving the Gaussian modified Pell sequence and Gaussian modified Pell polynomial sequence.
KeywordsModified Pell sequence, Modified Pell polynomial sequence, Gaussian modified Pell sequence, Gaussian modified Pell polynomial sequence.
In this paper, we introduce split Jacobsthal and split Jacobsthal-Lucas quaternions. We obtain generating functions and Binet's formulas for these quaternions. We also investigate some properties of them.
In this paper we define an equivalence relation on the set of all x J in order to form a basis for a new descent algebra of Weyl groups of type A n . By means of this, we construct a new commutative and semi-simple descent algebra of Weyl groups of type A n generated by equivalence classes arising from this equivalence relation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.