All Questions

How can we prove the following asymptotic lower bound for the regularized Beta function when $n\rightarrow\infty$? $$\int_0^{1} I_{2 t - t^2}\left(\frac{n - 1}{2}, \frac{1}{2}\right) dt=\Omega\left(\...

Let $F:[0,\infty) \to [0,\infty)$ be a $C^1$ strictly convex function. Let $\lambda_n \in [0,1],a_n\le c<b_n \in [0,\infty)$ satisfy $$ \lambda_n a_n +(1-\lambda_n)b_n=c_n \tag{1}$$ and assume that ...

I am not sure if this is exactly research-level, but I am struggling to find a proof for the following claim: Let $F:[0,\infty) \to [0,\infty)$ be a $C^2$ strictly convex function. Let $\lambda_n \in [...