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 Support may refer to: Arts, entertainment, and media * Supporting character Business and finance * Support (technical analysis) * Child support * Customer support * Income Support Construction * Support (structure), or lateral support, a ...

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 coefficient In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...

s along any row of

Pascal's triangle In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, althoug ...

and the elementary symmetric means of a finite sequence of real numbers.

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