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 −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.

Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials

“…In[2] Tulay Yagmur and Nusret Karaaslan are defined the Gaussian modified Pell numbers by the recurrence relation…”

On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers

“…There are other several studies dedicated to these sequences of Gaussian numbers such as the works in [1], [3], [4], [8], [9], [10], [12], [13], [16], [21], [22], [24], [25], [26], among others.…”

Gaussian Generalized Tetranacci Numbers

“…There are other several studies dedicated to these sequences of Gaussian numbers such as the works in [1], [3], [4], [8], [9], [10], [11], [13], [14], [15], [18], [23], [24], [25], [26], among others.…”