Prove that $f(z)$ is entire.
119869
Entire function and the series of its successive derivatives
75653
Prove that $|f ''|\ge 4$
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
7878
Proving that a doubly-periodic entire function $f$ is constant.
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
147270
Entire function. Prove that $f(\bar{z})=\overline{f(z)}, \forall z\in C$
69219
Prove there is a point $z\in[a,b]$ at which $f(z)=\frac{f(x_1)+f(x_2)+\cdots+f(x_k)}{k}$
92588
Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
20955
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
53627
Proving continuity of $f$
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
36379
Suppose that $ f $ is entire and that for each $ z $, either $ |f(z)| \leq 1 $ or $ |f^\prime (z) |\leq 1 $. Prove that $ f $ is a linear polynomial.
43177
How do I rigorously show $f(z)$ is analytic if and only if $\overline{f(\bar{z})}$ is?
60348
How do I prove $F(a)=F(a^2)?$
148486
Suppose $f$ is entire and $|f(z)| \leq A + B |z|^{3/2}$. Show that $f$ is a linear polynomial.
73454
Prove that $f$ has finite number of roots
138026
To show that $n!f(x) \in \mathbb{Z}[x]$