In mathematics, a sequence = of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if holds for . Remark: some authors (explicitly or not) add two further conditions in the definition of log-concave sequences: is non-negative has no internal zeros; in other words, the support of is an interval of . These conditions mirror the ones required for log-concave functions. Sequences that fulfill the three conditions are also called Pólya Frequency sequences of order 2 (PF2 sequences). Refer to chapter 2 of for a discussion on the two notions. For instance, the sequence satisfies the concavity inequalities but not the internal zeros condition. Examples of log-concave sequences are given by the binomial coefficients along any row of Pascal's triangle and the elementary symmetric means of a finite sequence of real numbers. References See also Unimodality Logarithmically concave function Logarithmically concave measure Sequences and series