Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence

Yıl 2018, Cilt: 2 Sayı: 1, 63 - 72, 30.06.2018

Tulay Yagmur Nusret Karaaslan

https://doi.org/10.29002/asujse.374128

Cited By: 6

Öz

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.

Anahtar Kelimeler

Modified Pell sequence, Modified Pell polynomial sequence, Gaussian modified Pell sequence, Gaussian modified Pell polynomial sequence

Kaynakça

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