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

S. E. Akrami

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

General Mathematics 2011-06-07 v2 Classical Analysis and ODEs

Authors: S. E. Akrami

Abstract

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 $\R$ .

Keywords

series expansion analytic functions convergence nowhere analytic functions dense subset

Cite

@article{arxiv.1105.2611,
  title  = {On the Series $\sum_{n=0}^\infty t^nf^{(n)}(t) (-1)^n/n!$},
  author = {S. E. Akrami},
  journal= {arXiv preprint arXiv:1105.2611},
  year   = {2011}
}

Comments

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

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

Abstract

Keywords

Cite

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