## On Fibonacci functions with Fibonacci numbers

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##### Date

2012

##### Journal Title

##### Journal ISSN

##### Volume Title

##### Publisher

Springer

##### Abstract

In this paper we consider Fibonacci functions on the real numbers R, i.e., functions f : R -> R such that for all x is an element of R, f(x + 2) = f(x + 1) + f(x). We develop the notion of Fibonacci functions using the concept of f f-even and f-odd functions. Moreover, we show that if f is a Fibonacci function then lim(x ->infinity) f(x+1)/f(x) = 1+root 5/2.

##### Description

##### Keywords

Fibonacci function, f-even (f-odd) function, Golden ratio, Mathematics, Applied, Mathematics

##### Citation

Han, J., Kim, H., Neggers, J. (2012): On Fibonacci Functions with Fibonacci Numbers. Advances in Difference Equations. Article Number 126.