## You are here

Homef cannot be analytically continued onto a disk

## Primary tabs

# f cannot be analytically continued onto a disk

LaTeX field for this problem:

Let $f(z)=\sum_{{n=0}}^{{\infty}}a(n)z^{n}$ have radius of convergence $1$
and assume that $0\leq a(n)$ for all $n=0,1,2,\ldots$. Prove that the
point $z=1$ is a singular point^{}. That is, prove that $f$ cannot be
analytically continued onto a disk centered at $z=1$ and having a positive radius.

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections