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 28 Evaluating $\lim\limits_{n\to\infty} \sum_{k=1}^{n^2} \frac{n}{n^2+k^2}$ 22 Infinite product of sine function 19 Compute: $\lim_{n\to\infty}\frac{{\left(1^1 \cdot 2^2 \cdot3^3\cdots n^n\right)}^\frac{1}{n^2}}{\sqrt{n}}$ 18 if $f$ is entire and $|f(z)| \leq 1+|z|^{1/2}$, why must $f$ be constant? 18 Calculating the shortest possible distance between points

# 36,110 Reputation

 +30 How to show $\sum_{n=1}^{\infty} \frac{1}{n^{3} \binom{2n}{n}} = 4 \int_{0}^{\frac{1}{2}} \frac{\arcsin^{2}(x)}{x} \ dx$? +10 Countable total subset in $\ell^\infty/ c_0$ +10 Relations between p norms +10 Surely You're Joking, Mr. Feynman! $\int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}\,dx$

# 45 Questions

 33 Continuous projections in $\ell_1$ with norm $>1$ 19 Computing $\lim\limits_{n\to+\infty}n\int_{0}^{\pi/2}xf(x)\cos ^n xdx$ 17 Solving functional equation $f(x)^2+f(y)^2=f(x+y)(f(f(x))+f(y))$ 14 Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? 14 Minmax problem for polygons

# 179 Tags

 872 functional-analysis × 427 225 banach-spaces × 114 427 real-analysis × 146 187 limits × 39 426 calculus × 90 170 operator-theory × 90 237 sequences-and-series × 55 149 measure-theory × 65 235 integration × 57 131 analysis × 55

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