A polynomial is called logarithmically concave (or log-concave) if the sequence of its coefficients is logarithmically concave.
If
is log-convex and is unimodal, then
is unimodal. However, the product of two log-convex
polynomials is itself log-convex (Levit and Mandrescu 2005).
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.
is log-convex and 
is unimodal, then
is unimodal. However, the product of two log-convex
polynomials is itself log-convex (Levit and Mandrescu 2005).
