On the k- Pell Quaternions and the k- Pell-Lucas Quaternions

Abstract

The quaternions form a four-dimensional associative and non-commutative algebra over the set of

real numbers. In this paper, firstly, we give some relations for k - Pell quaternions and k - Pell-Lucas quaternions.

Then, by using Binet’s formula, we obtain their sums formulas, their the identities such as Cassini’s identity and

generating function, also derive relationships between these quaternions.

Keywords

• k - Pell numbers,k - Pell-Lucas numbers,quaternions

k- Pell Kuaterniyonlar ve k- Pell-Lucas Kuaterniyonlar Üzerine

Abstract

Kuaterniyonlar, reel sayılar kümesinde dört boyutlu birleşmeli ve değişmeli olmayan bir cebir oluştururlar.

Bu makalede ilk olarak, k - Pell kuaterniyonlar ve k - Pell-Lucas kuaterniyonların bazı bağıntılarını verdik. Daha

sonra, Binet formülünü kullanarak toplam formüllerini, Cassini özdeşliği ve geren fonksiyonu gibi özdeşliklerini

elde ettik, ayrıca bu kuaterniyonların arasındaki ilişkileri türettik.

Keywords

• k - Pell sayıları,k - Pell-Lucas sayıları,kuaterniyonlar

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