On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications

Abstract

We define the Gauss Fibonacci polynomials. Then we give a formula for the Gauss Fibonacci polynomials by using the Fibonacci polynomials. The Gauss Lucas polynomials are described and the relation with Lucas polynomials are explained. We show that there is a relation between the Gauss Fibonacci polynomials and the Fibonacci polynomials. The Gauss Lucas polynomials are also given by using the Gauss Fibonacci polynomials. Some theorems like Cassini’s theorem are proved for the polynomials. Their Binet’s formulas are obtained. We also define the matrices of the Gauss Fibonacci polynomials and the Gauss Lucas polynomials. We examine properties of the matrices.

Keywords:

• Fibonacci polynomials
• Gauss Fibonacci numbers
• Gauss Lucas numbers
• Lucas polynomials

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 11B39
• 11B83
• Secondary 11C20