Padovan, Perrin and Pell-Padovan Dual Quaternions

Abstract

In this present study, we intend to determine the Padovan, Perrin and Pell-Padovan dual quaternions with nonnegative and negative subscripts. In line with this purpose, we construct some new properties such as; special determinant equalities, new recurrence relations, matrix formulas, Binet-like formulas, generating functions, exponential generating functions, summation formulas, and binomial properties for these special dual quaternions.