A finite sequence of real numbers is said to be logarithmically concave (or log-concave) if
holds for every with .
A logarithmically concave sequence of positive numbers is also unimodal.
If and are two positive log-concave sequences of the same length, then is also log-concave. In addition, if the polynomial has all its zeros real, then the sequence is log-concave (Levit and Mandrescu 2005).
An example of a logarithmically concave sequence is the sequence of binomial coefficients for fixed and .