We study the series $\sum_{ n=0}^{ \infty}\frac{ (-1)^n}{ n!}t^nf^{ (n)}(t)$. We show that for analytic functions this series is uniformly and absolutely convergent to the constant $f(0)$. We show that there are nowhere analytic functions for them the series is divergent for all $t$ and also there are nowhere analytic functions for them the series is convergent to $f(0)$ at least for $t$ in a dense subset of $\R$.
Categories: math.GM math.CA