# Questions tagged [analytic-functions]

For questions about analytic functions, which are real or complex functions locally given by a convergent power series.

1,087 questions
Filter by
Sorted by
Tagged with
11 views

20 views

25 views

### complex function continuous but not differentiable on an open set

Could one possibly come up with an example of a complex-valued function such that $f(z)$ is continuous on the open set $D=\{ z \in \mathbb{C}:z \neq 0 \}$ and $\lim\limits_{z\to 0} f(z) = \infty$ but ...
### Proving that $\lambda$ is not analytic in differential topology.
Let $\lambda : \mathbb{R} \to \mathbb{R}$ be defined by $\lambda(t) =\begin{cases} 0, & \text{for } t \leq 0 \\ e^{-1/t}, & \text{for } t > 0. \end{cases}$ This is a smooth function with ...
### Analytic continuation of $y=\sqrt{x^4-x^2+1}$
Question. Consider the function $y=\sqrt{x^4-x^2+1}$. Consider a sufficiently large circle $C$ of $0$ in $\mathbb{C}$, and let $x_0$ lies in this circle (suppose $x$ is not a branch point of this ...