Tagged Questions
0
votes
1answer
38 views
Zeros of the analytic limit of complex polynomials
For $n\in\mathbb{N}$ let $p_n$ be a polynomial of degree $n$.
Suppose there exists $c>0$ such that
$\bullet$ if $z\in\mathbb{C}$ is a zero of a $p_n$, then $|z^2+c|\leq c$ (note that in particular ...
1
vote
2answers
59 views
Removable singularity and laurent series
How to show $z=\pm\pi$ is a removable singularity for $\frac1{\sin z}+\frac{2z}{z^2-\pi^2}$?
I tried to compute the Laurent series, specifically the coefficients for $1/z,1/z^2,...$ since if we can ...
2
votes
1answer
63 views
Analyticity of $\frac{Log(z+4)}{z^2+i}$
This problem is from Churchill and Brown. How do I prove that
$f(z)=\frac{Log(z+4)}{z^2+i}$ is analytics everywhere except $\pm\frac{(1-i)}{\sqrt{2}}$ and on the portion $x \le -4$ of the real axis.
...
5
votes
4answers
447 views
How many smooth functions are non-analytic?
We know from example that not all smooth (infinitely differentiable) functions are analytic (equal to their Taylor expansion at all points). However, the examples on the linked page seem rather ...
