Which entire functions $h(z)$ can be written as $h(z)=f(z+1)-f(z)$ for some entire function $f$?
137971
Existence of an holomorphic function
124971
Find all holomorphic functions with $\Re(f(x+iy))=2xy$
20790
What are irreducibles in the ring $R$ of entire functions?
5625
Entire function with vanishing derivatives?
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
133427
analytic function on $\mathbb{C}$ such that $f\Bigl(\frac{1}{2n}\Bigr)=f\Bigl(\frac{1}{2n+1}\Bigr)=\frac{1}{2n}$
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
133099
Decomposition of holomorphic function as a sum of entire functions
17508
Knowing $|z|$ and $|w|$ (and possibly $z\overline{w}$), what are $|z+w|^2$, $|zw|^2$, $|z-w|^2$, $|z/w|^2$?
86473
Find all entire functions such that $|f(z)|\leq |\sin(z)|$ for all $z\in\mathbb C$.
10389
Does there exist an holomorphic function such that $|f(z)|\geq \frac{1}{\sqrt{|z|}}$?
23465
When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?
1071
Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)
27251
Holomorphic function with $f\circ f=f$
139168
Prove that there is an unique $z$ s.t. $f(z) = z$ where $z$ is a complex number
26353
Can any harmonic function on $\{z:0<|z|<1\}$ be extended to $z=0$?
66867
Question regarding the function $z=a+bi \mapsto f(z)=a+i(a+b)$.