All Questions

I was looking at the definition of log-concavity: A function $F:\mathbb{R}^n\rightarrow\mathbb{R}$ is said log-concave iff $F(x)\geq 0\forall x\in\mathbb{R}^n$ and $$F(x)^\lambda F(y)^{1-\lambda}\leq ...

I have functions $A, B, F, S$ that are zero on $(-\infty, 0)$. And I have successfully represented the below equation as convolution and multiplication: $\int_0^t {dt_1} \int_0^t {dt_2} B(t - t_2)F(...

This is just a summer-time curiosity arisen after a recent question by Dominic van der Zypen. For a finite subset $S$ of $\mathbb{Z}\times\mathbb{Z}$ and a function $f$ on $\mathbb{Z}\times\mathbb{...

Please, help me to understand following convolution (or give a reference): $$ \sum_{R=0}^N \binom{R}{r} \binom{N-R}{n-r} = \binom{N+1}{n+1} $$ Why is it true? Thank you!