Abstract In this paper, we introduce and study the Pell, Pell-Lucas, and r -Pell elliptic quaternions. We give the ordinary generating functions, the Binet-type formulas, general bilinear index-reduction formulas, and the convolution identities for these quaternions. Finally, we define the Pell and Pell-Lucas elliptic quaternion polynomials of one and two variables.
Bród et al. (Wed,) studied this question.