Just noticed, this is the wrong place for the topic to be... Could one of the administrators please move this thread to the "inequalities" section?
Fix and consider the function .Originally Posted by Rebesques
Then f(0) = 1, , and both g(x) and h(x) are log-concave (that is, their logarithms are concave down). It is known that the sum of log-concave functions is also log-concave, so f is log-concave. As a consequence,