If the $n$-th derivative of analytic function is $0$, then it's a polynomial
65619
Does $f^{(n)} = 0$ imply that complex $f$ is a polynomial?
111760
If $f^2$ is an analytic function then so is $f$
64172
Show that if $f$ is analytic in a domain $D$ and $|f(z)|$ is constant in $D$, then the function $f(z)$ is constant in $D$
141983
Complex polynomial of degree $n$
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
103340
Show that this entire function is polynomial.
124459
$n^{th}$ derivative of a tetration function
6722
to show $f$ is a polynomial in $z$
148247
Prove the existence of an analytic function
153406
$[F(t):F(t^n)]=n$ where $t$ is trascendental
71094
Proof that 1-1 analytic functions have nonzero derivative
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
132663
Show $f$ is analytic if $f^8$ is analytic
133580
Nth derivative of $x^x$
87743
Is a function whose derivative vanishes at rationals constant?
4813
On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?)
14759
Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.