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

On the Series $\sum_{n=0}^\infty t^nf^{(n)}(t) (-1)^n/n!$