Binomials transformation formulae for scaled Fibonacci numbers

Abstract

The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.

Keywords

• δ-fibonacci numbers
• δ-lucas numbers
• binomial transformation
• llb39
• llb83