On the linear (in)dependence of sequences of derivatives of the functions $x^n\sin x$ and $x^n\cos x$

Jozef Fecenko, Enno Diekema

The main goal of the paper is to prove that the sequence of functions $f(x),Df(x),\dots ,D^{2n+1}f(x)$, where $f(x)$ is $x^n\sin x$ or $x^n\cos x$ are linearly independent. Or mo…