log-concave sequence

A finite sequence of real numbers {a_k}_(k = 1)^n is said to be logarithmically concave (or log-concave) if a_i^2>=a_(i - 1) a_(i + 1) holds for every a_i with 1<=i<=n - 1. A logarithmically concave sequence of positive numbers is also unimodal. If {a_i} and {b_i} are two positive log-concave sequences of the same length, then {a_i b_i} is also log-concave. In addition, if the polynomial sum_(i = 0)^n p_i x^i has all its zeros real, then the sequence {p_i/(n i)} is log-concave.

logarithmically concave function | logarithmically concave polynomial | unimodal sequence