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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 $\sum_{n \in \mathbb{Z}} \ln(|x - n|)$?