# zbMATH — the first resource for mathematics

Generalized transformations on ratios of Fibonacci and Lucas numbers. (English) Zbl 0860.11006
The authors consider generalized Fibonacci sequences $$(u_n)$$ and generalized Lucas sequences $$(v_n)$$, both satisfying the recurrence $$x_{n+1} = px_n- qx_{n-1}$$. They study the behaviour of the quotients $$\left( {u_{n+d} \over u_n} \right)$$ under transformations of the Newton type $N(x)= x-{f(x) \over f'(x)} \quad \text{with} \quad f(x)= x^2-v_dx+ q^d.$ Extensions of the well-known formula $N \left({u_{n+d} \over u_n} \right)= {u_{2n +d} \over u_{2n}}$ are shown.
Reviewer: R.F.Tichy (Graz)
##### MSC:
 11B39 Fibonacci and Lucas numbers and polynomials and generalizations