Copper Fibonacci, Copper Lucas polynomials and their some special transformations and hyperbolic quaternions

In this study, we define the Copper Fibonacci and Copper Lucas polynomials, and some terms of these polynomials are given, including the relationship of the ratio of the biggest to the smallest of two consecutive terms of these polynomials. In addition, we provide important relations among the positive and negative index terms, and the sum of the squares of two consecutive terms is related to these polynomials. We apply Catalan transformations to these polynomials and obtain some of their terms. We also relate the terms of the Hankel transformation of the Catalan Copper Fibonacci polynomials with the classical Fibonacci numbers. Finally, we define the application of the Copper Fibonacci and Copper Lucas polynomials to hyperbolic quaternions. © Indian National Science Academy 2025.