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 .

Levit, V. E. and Mandrescu, E. "The Independence Polynomial of a Graph--A Survey." In Proceedings of the 1st International
Conference on Algebraic Informatics. Held in Thessaloniki, October 20-23, 2005
(Ed. S. Bozapalidis, A. Kalampakas, and G. Rahonis). Thessaloniki,
Greece: Aristotle Univ., pp. 233-254, 2005.