Gaussian Pell and Gaussian Pell-Lucas Quaternions

The main aim of this work is to introduce the Gaussian Pell quaternion QGp(n) and Gaussian Pell-Lucas quaternion OGq(n), where the components of QGp(n) and QGq(n) are Pell numbers p(n) and Pell-Lucas numbers q(n), respectively. Firstly, we obtain the recurrence relations and Binet formulas for QGp(n) and QGq(n). We use Binet formulas to prove Cassini's identity for these quaternions. Furthermore, we give some basic identities for QGp(n) and OGq(n) such as some summation formulas, the terms with negative indices and the generating functions for these complex quaternions.