%0 Journal Article %1 Giacomelli2011 %A Giacomelli, Piero %D 2011 %E arxiv, %K Log-concavity Lucas Sequences %T Log-concavity of Lucas Sequences of first kind %U http://arxiv.org/abs/1101.1805 %X 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.

@article{Giacomelli2011, abstract = { 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. }, added-at = {2011-01-13T12:39:43.000+0100}, author = {Giacomelli, Piero}, biburl = {https://www.bibsonomy.org/bibtex/290a978556512f9d4cc8db63cbe37ec3c/pgiacome}, description = {Log-concavity of Lucas Sequences of first kind}, editor = {arxiv}, interhash = {26c739f5e0c2ca06084300bc5285fc3b}, intrahash = {90a978556512f9d4cc8db63cbe37ec3c}, keywords = {Log-concavity Lucas Sequences}, note = {cite arxiv:1101.1805 }, timestamp = {2011-01-13T12:39:43.000+0100}, title = {Log-concavity of Lucas Sequences of first kind}, url = {http://arxiv.org/abs/1101.1805}, year = 2011 }