Show if there is an analytic function $f \in \mathbb{C}$ such that $f\left(\frac{1}{n}\right)=\frac{n}{1+n}$
131999
Can a holomorphic function satisfy $f(1/n)=1/(n+1)$?
89050
If $|f(z)|\leq |f(z^2)|$ on the unit disk, show that $f$ is a constant function.
82229
Show if complex function $f(z)$ contains all real coefficients then $f(\bar z)$ = $\bar {f(z)}$
25921
Show that $\left(1+\dfrac{1}{n}\right)^n$ is monotonically increasing
94680
Holomorphic function $f$ such that $f'(z_0) \neq 0$
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
150124
Holomorphic function such that $f(\frac{1}{n})=\frac{1}{n+1}$.
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
63446
The existence of analytical branch of the logarithm of a holomorphic function
46514
Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic
148247
Prove the existence of an analytic function
64748
analytic in open unit disk,corresponding to a bounded sequence and a bounded functional sequence
80826
To prove $\left|\frac{p_n(z)}{q_m(z)}\right|\leq \frac{M}{|z|^{m-n}}$ for some $M>0$
68854
Proving $\mathcal{F}\left(\frac{d^n}{dx^n} f(x)\right)=(ik)^n\mathcal{F}(f(x))$.
3349
For $f$ an analytic function, what is
142928
Proving $\left\{ \frac{1}{n} \right\}$ is Cauchy
69219
Prove there is a point $z\in[a,b]$ at which $f(z)=\frac{f(x_1)+f(x_2)+\cdots+f(x_k)}{k}$