All Questions

Let $k,n,m$ be positive integers and suppose that $f$ is $C^{k}(\mathbb{R}^n,\mathbb{R}^m)$ functions. For any given $\epsilon>0$ and $x_0\in \mathbb{R}^n$, are there known sharp approximation ...

I have encountered in a problem some polynomials given by $P_k(x) = \prod_{j=0}^{k-2} (kx-j)$. I need to understand if these polynomials are known, and if they have certain special properties, as ...

I'm in trouble understanding this theorem: For a given function, differentiable n times at a given point $x_0$, there exist a unique polynomial $P_n$ (of degree $\le$n) such that $$\forall \; k=0,...,...