2011/01/10 by Piero Giacomelli, Giacomelli, Piero
Physics and Astronomy · Mathematics · #Advanced Mathematical Theories and Applications #Advanced Combinatorial Mathematics #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.1101.1805
In these notes we address the study of the log-concave operator acting on Lucas Sequences of first kind. We will find for which initial values a generic Lucas sequence is log-concave, and using this we show when the same sequence is infinite log-concave. The main result will help to find the log-concavity of some well known recurrent sequences like Fibonacci and Mersenne. Some possible generalization for a complete classification of the log-concave operator applied to general linear recurrent sequences is proposed.