Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence
Journal: Aksaray University Journal of Science and Engineering (Vol.2, No. 1)Publication Date: 2018-06-30
Authors : Tulay Yagmur Nusret Karaaslan;
Page : 63-72
Keywords : Modified Pell sequence; Modified Pell polynomial sequence; Gaussian modified Pell sequence; Gaussian modified Pell polynomial sequence;
Abstract
In this paper, we first define the Gaussian modified Pell sequence, for n ≥ 2, by the relation = 2 + with initial conditions = 1 ─ i and = 1 + i. Then we give the definition of the Gaussian modified Pell polynomial sequence, for n ≥ 2, by the relation = 2 + with initial conditions = 1─ xi and = 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.
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