Analytic function with $f(z)=z$ for all $z$
49155
$f: \Omega \rightarrow \Omega$ holomorphic, $f(0) = 0$, $f'(0) = 1$ implies $f(z) = z$
141254
Zeros of analytic function of several real variables
123249
An analytic function $f$ on $|z|<1$ with $\sup_{|z|<1} |f(z)|=1$ and $|f(0)|=\frac{1}{2}$ has no zeros in $|z|<\frac{1}{2}$
53338
Analytic functions with nonessential singularity at infinity must be a polynomial
80650
Complex differentiability of $f(z)=|z|$
111635
Show that if $f(z)$ is a continuous function on a domain $D$ such that $f(z)^N$ is analytic for some integer $N$, then $f(z)$ is analytic on $D$.
82079
Holomorphic function satisfying $f^{-1}(\Bbb R)=\Bbb R$ is of the form $f(z)=az+b$
43177
How do I rigorously show $f(z)$ is analytic if and only if $\overline{f(\bar{z})}$ is?
155531
Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
133333
Find $f(x)$ for $f(f(x))=\sin x$
133427
analytic function on $\mathbb{C}$ such that $f\Bigl(\frac{1}{2n}\Bigr)=f\Bigl(\frac{1}{2n+1}\Bigr)=\frac{1}{2n}$
82229
Show if complex function $f(z)$ contains all real coefficients then $f(\bar z)$ = $\bar {f(z)}$
25633
Is the function $f(z)=xy+iy$ analytic?
148474
on the boundary of analytic functions
62901
Bound for Analytic Function on Unit Disk
14759
Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$