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May
1
awarded  Autobiographer
Apr
30
comment Can gauss quadrature integrate this function exactly $f(x) = \frac{2x}{\sqrt{x^3 + 2x + 5}}$?
Did you use wolfram? If not, what particular formula did you use?
Apr
30
comment Can gauss quadrature integrate this function exactly $f(x) = \frac{2x}{\sqrt{x^3 + 2x + 5}}$?
Nevermind......
Apr
30
asked Can gauss quadrature integrate this function exactly $f(x) = \frac{2x}{\sqrt{x^3 + 2x + 5}}$?
Apr
25
comment Where does this inequality come from: $\frac{|f(x) - f(x-h)|}{h} \le ||f'||_{L^\infty(x, x-1)}$?
That's fine, makes perfect sense now!
Apr
25
asked Where does this inequality come from: $\frac{|f(x) - f(x-h)|}{h} \le ||f'||_{L^\infty(x, x-1)}$?
Apr
25
accepted Intuition for separable spaces?
Apr
15
accepted Are there identities which will make calculating $\Delta \frac{e^{ik|x|}}{|x|}$ more efficient and clearer?
Apr
15
comment Are there identities which will make calculating $\Delta \frac{e^{ik|x|}}{|x|}$ more efficient and clearer?
@C.Dubussy Thanks. As expected it came out as $-k^2 \Delta \frac{e^{ik|x|}}{|x|}$. I wonder if there are other identities for it...considering how cleanly it ends up?
Apr
15
asked Are there identities which will make calculating $\Delta \frac{e^{ik|x|}}{|x|}$ more efficient and clearer?
Apr
14
comment Stuck while trying to show fundamental solution $\frac{1}{2\pi}\ln|x|$ satisfies $\Delta \phi(x) = \delta(x)$ in 2d?
@Hajo Yes that is the case.
Apr
14
asked Stuck while trying to show fundamental solution $\frac{1}{2\pi}\ln|x|$ satisfies $\Delta \phi(x) = \delta(x)$ in 2d?
Apr
10
accepted What does a single eigenvector and eigenvalue for a $2 \times 2$ matrix represent geometrically?
Apr
10
accepted Can you take the limit as $x \to \infty$ of an expression such as $\sum_{n \in \mathbb{Z}} \ln(|x - n|)$?
Apr
9
comment Intuition for separable spaces?
@Math1000 You lost me at 'Lindelof space' lol!
Apr
9
comment $L^p$ and $L^q$ space inclusion
I don't see how you can just pick one subsequence in step 1 that converges to bot $f$ and $g$. It seems you can you just pick one for $f$ (or $g$), using Theorem 4.9 in Breviz, but how can you pick one that converges to both?
Apr
9
comment Intuition for separable spaces?
Thanks, these are exactly the kind of answers I was looking for! ...one thing though, aren't the reals separable because the rationals form a countable dense subspace of $\mathbb{R}$...'dense' makes it sounds like there is 'a lot of stuff' in the space?
Apr
9
asked Intuition for separable spaces?
Apr
5
comment Can you take the limit as $x \to \infty$ of an expression such as $\sum_{n \in \mathbb{Z}} \ln(|x - n|)$?
Well $x \in \mathbb{R}$. It seems to me like we can't even get as far as saying its divergent because it cant be evaluated...ie. we can't evaluate all the terms and therefore we can't evaluate the expression itself? $\dots + \lim_{x \to \infty} \ln(|x - (-1)|) + \lim_{x \to \infty} \ln(|x|) + \lim_{x \to \infty} \ln(|x - 1|) + \lim_{x \to \infty} \ln(|x - 2|) + \lim_{x \to \infty} \ln(|x - 3|) + \dots$ doesn't seem to make sense as we can't evaluate all the terms?!
Apr
5
asked Can you take the limit as $x \to \infty$ of an expression such as $\sum_{n \in \mathbb{Z}} \ln(|x - n|)$?