2 research outputs found
On the existence of ratio limits of weighted -generalized Fibonacci sequences with arbitrary initial conditions
We study ratio limits of the consecutive terms of weighted -generalized
Fibonacci sequences generated from arbitrary complex initial conditions by
linear recurrences with arbitrary complex weights. We prove that if the
characteristic polynomial of such a linear recurrence is asymptotically simple,
then the ratio limit exists for any sequence generated from arbitrary
nontrivial initial conditions and it is equal to the unique zero of the
characteristic polynomial.Comment: 3 page
A necessary and sufficient criterion for the existence of ratio limits of sequences generated by linear recurrences
We introduce a necessary and sufficient criterion for determining the
existence and the values of ratio limits of complex sequences generated by
arbitrary linear recurrences