All questions with tag [math: analytic-functions]


$f$ is analytic on $D$ if and only if $f$ is $n$ times continuously differentiable on $D$?

Suppose I have an actual - valued function $f$ specified on a facility open linked set $D$ . Am I right in claiming that: $f$ is analytic on $D$ if and also just if $f$ is $n$ times continually differentiable on $D$ ? Or does this just use if $f$ is intricate valued? many thanks
2022-06-06 17:52:28

Finding an entire function such that $|f(z)| > e^{Im f(z)}$ and $f(0)=2$ & an analytic function that has an essential singularity at $z=0$

Here are my troubles: Find a whole function $f(z)$ such that $|f(z)| &gt; e^{\operatorname{Im} f(z)}$ for all $z \in \mathbb{C}$ and also $f(0)=2$ I am attempting to presume $2\cos(z), 2e^z$ , etc, yet they are all fallen short ultimately. < ol start = "2" > Let $f(z)$ be analytic in the pierced disk $0&lt;|...
2022-06-06 17:48:48