Real image (such as the images on the right), real rays of light are always represented by full, solid lines; perceived or extrapolated rays of light are represented by dashed lines. A real image occurs where rays converge, whereas a virtual image occurs where rays only "appear" to converge. Real images can be produced by concave mirrors and converging lenses, only if the object is placed further away from the mirror/lens than the focal point and this real image is inverted. As the object approaches the focal point the image approaches infinity, and when the object passes the focal point the image
Logarithmically concave sequence 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. Logarithmically concave sequence 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 hypotheses in the definition of log-concave sequences: These hypotheses mirror the ones required for log-concave functions. Sequences that fulfill the three conditions are also called Pòlya Frequency sequences of order 2 (PF sequences). Refer to chapter 2 of for