# Tagged Questions

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### Uniform convergence of a sequence of polynomial logarithm

Let $P\in \Bbb{C}[X]$ of degree $d\ge 2$. For $n\in \Bbb{N}$ (include $O$). Denote by $P^n$ the $n$-th composition and $g_n: z\mapsto \frac{1}{d^n}\log(\max \{1,\vert P^n\vert\})$. Show that ...
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### Series of polynomials and uniformly convergence

It's part of the proof of a Lemma of an article I was reading (Algebraic values of transcendental functions at algebraic points). I couldn't understanding one thing: Let f be a complex function such ...
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### Closed form of a sum of binomial coefficients?

I have the following function: $T_n(d)=\sum\limits_{k=\frac{n-d}{2}}^{\lceil \frac{n}{2} \rceil}{k\choose \frac{n-d}{2}}$ ${n \choose 2k}$, where $n,d\in \mathbb{N}^0$, and $n,d$ have the same ...
So this is a 2-part question (both parts I believe are closely related): How exactly does on express the sum $$\sum_{i=0}^{k}{i^n} = Q(n,k)$$ in a closed form For arbitrary positive integers ...