Gaussian Modified Pell Sequence and 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. W e 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.