Determine all entire functions $f$ with $\Re f(z) > 0$ for all $z \in \mathbb{C}$ such that, $f(0) = 1$.
17408
An entire function whose real part is bounded must be constant.
94597
$f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$
8179
If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
62568
Does there exists an entire function $f: \mathbb C \to \mathbb C$ which is bounded on real line and imaginary line?
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
128477
Entire function constant, where $f(z)=f(z+1)$ and $|f(z)|< e^{|z|}$.
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
65054
How is $e^z$ the only function that is entire with the property $f'(z) = f(z)$ and $f(0) = 1$
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
58178
Property of Entire Functions
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
122356
Complex Analysis, Entire functions
155444
Show that entire function $f$ is a polynomial of degree at most $n$
30855
Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.
73419
For $f$ entire and $\{f(kz) : k \in \mathbb{C}\}$ a normal family, prove that $f$ is a polynomial.