Here's a little troublesome inequality: Prove that
I would appreciate a shorter solution, but with less theory involved... Asking 2 much?
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,