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

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

2011-05-13

arxiv.org/abs/1105.2611v2

Mathematics

General Mathematics

12 pages. Second Version (June 05, 2011):Some new examples has been added to the previous version

Scientific paper

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 $\R$.

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