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923 Answers

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82
Relations between p norms
Oct 21 '12 at 16:45
57
Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$
Jun 12 '12 at 13:58
33
$\ell^p\subseteq\ell^q$ for $0<p<q<\infty$ and $\|\cdot\|_q<\|\cdot\|_p$
Feb 29 '12 at 1:43
32
Evaluating $ \lim\limits_{n\to\infty} \sum_{k=1}^{n^2} \frac{n}{n^2+k^2} $
Sep 4 '12 at 14:25
31
How to show that quotient space $X/Y$ is complete when $X$ is Banach space, and $Y$ is a closed subspace of $X$?
Mar 3 '13 at 22:56
29
Surely You're Joking, Mr. Feynman! $\int_0^\infty\frac{\sin^2x}{x^2(1+x^2)}\,dx$
May 21 '14 at 12:41
26
Compute the limit of $\frac1{\sqrt{n}}\left(1^1 \cdot 2^2 \cdot3^3\cdots n^n\right)^{1/n^2}$
Jun 23 '12 at 20:30
25
Gelfand Topology and C*-algebras
Feb 17 '13 at 22:32
24
Prove that $X'$ is a Banach space
Apr 14 '12 at 20:19
23
Inequality. $a^2+b^2+c^2 \geq a+b+c$
Aug 12 '12 at 12:18
20
Why study operator spaces?
Sep 26 '13 at 22:26
20
if $f$ is entire and $|f(z)| \leq 1+|z|^{1/2}$, why must $f$ be constant?
May 30 '12 at 19:13
20
Evaluation of the limit $\lim\limits_{n \to \infty } \frac1{\sqrt n}\left(1 + \frac1{\sqrt 2 }+\frac1{\sqrt 3 }+\cdots+\frac1{\sqrt n } \right)$
Nov 16 '12 at 16:38
19
Weak Convergence implies boundedness and componentwise convergence
Oct 15 '12 at 15:04
19
How to prove: $\left(\frac{2}{\sqrt{4-3\sqrt[4]{5}+2\sqrt[4]{25}-\sqrt[4]{125}}}-1\right)^{4}=5$?
Aug 10 '14 at 8:18
18
Why isometric isomorphic between Banach spaces means we can identify them?
May 16 '13 at 22:05
18
Calculating the shortest possible distance between points
Jun 3 '12 at 10:51
17
Evaluate $\int_{0}^{\infty} \frac{{(1+x)}^{-n}}{\log^2 x+\pi^2} \ dx, \space n\ge1$
Oct 6 '12 at 19:58
17
Maclaurin expansion of $\arcsin x$
Sep 17 '12 at 5:18
17
Non-closed subspace of a Banach space
Aug 2 '12 at 9:39
17
How to evaluate $ \lim \limits_{n\to \infty} \sum \limits_ {k=1}^n \frac{k^n}{n^n}$?
Jun 28 '12 at 8:51
16
Properties of reflexive Banach spaces
Aug 4 '14 at 16:07
16
Why is $L^1(\mathbb{R}^n) \cap L^2(\mathbb{R}^n)$ dense in $ L^2(\mathbb{R}^n)$?
Dec 27 '12 at 20:36
16
Why do we distinguish the continuous spectrum and the residual spectrum?
Jul 24 '12 at 20:41
16
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
Jul 14 '12 at 18:38
15
Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$
Oct 8 '12 at 7:50
15
Continuity of the adjoint map in various operator topologies
Aug 23 '13 at 15:29
14
How to calculate $\int_{-a}^{a} \sqrt{a^2-x^2}\ln(\sqrt{a^2-x^2})\mathrm{dx}$
Jul 9 '12 at 16:47
14
How to solve an exponential equation with two different bases: $3^x - 2^x = 5$
Apr 2 '12 at 22:12
14
What are the Wolfram Mathematica NDSolve function methods?
Nov 17 '11 at 19:43
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