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9h
comment Why is the standard inner product on F^n equal to this?
Otherwise the mnemonic "coordinates always columns" would fail. :-)
1d
comment given $-\pi < \theta \leq \pi$ prove $f(z) = z^{1/3}$ is not entire.
It's not even continuous (along the negative real axis).
2d
reviewed Reject application of L'Hopital's rule?
Feb
4
comment What is a special function?
Here's Michael Berry's answer: ega-math.narod.ru/Nquant/Berry.htm
Feb
3
comment Showing $\int_{1}^{0}\dfrac{\ln(1-x)}{x}dx=\dfrac{\pi ^{2}}{6}$
I suspect that this is just what the OP meant by "using the Riemann zeta function"... (I.e., using that we know that $\zeta(2)=\pi^2/6$.)
Feb
3
answered Showing $\int_{1}^{0}\dfrac{\ln(1-x)}{x}dx=\dfrac{\pi ^{2}}{6}$
Feb
2
comment Integral of $x^{-2}e^x$
$e^x/x^2$ on its own doesn't have an elementary antiderivative.
Jan
29
comment Why is it that in the parametrization of a line, the point $P_0$ is indicated with brackets and not parenthesis?
None that I can think of right now anyway...
Jan
29
comment Why is it that in the parametrization of a line, the point $P_0$ is indicated with brackets and not parenthesis?
I also prefer (1), but that requires the operation "point+vector=point", which most books (for some reason) seem reluctant to introduce. If you want to stick to the old familiar operation "vector+vector=vector", then there is no choice but to introduce an origin $O$ and the vector $\vec{OP}$.
Jan
26
comment Trigonometric Expression for $1 + \cos \alpha + \cos 2\alpha + \cdots + \cos n \alpha$ using complex numbers
Related: math.stackexchange.com/questions/17966/…
Jan
24
awarded  Enlightened
Jan
24
awarded  Nice Answer
Jan
22
comment Expected length of longest increasing subsequence of a random sequence
See Lemma 1.4 on p. 9 in Dan Romik's book, which you can download from his homepage: math.ucdavis.edu/~romik/book
Jan
17
comment Is this strange function differentiable?
@MarcoIntini: That's not a good idea, since unless you know in advance that $\partial_x f$ is continuous at the origin (which you don't), there is no guarantee that the limit of $\partial_x f$ as $(x,y)\to(0,0)$ agrees with the actual value $\partial_x f(0,0)$.
Jan
16
comment Does $[0.9999…]=1$?
@sinbadh: You mean "not continuous on $\mathbb{R}$". And I think this is precisely what the OP's confusion is about; it only appears to be contradition if one believes that all functions must be continuous, so that one can always interchange the order of the operations "applying the function" and "taking the limit".
Jan
11
comment Gimbal lock easier to control with quaternions?
Why the tag "singular-cas"?
Jan
8
comment How to evaluate this definite integral: $\int_3^6 \frac{\sqrt x}{\sqrt x+\sqrt{9-x}} dx$
Check out Nelsen's short paper Symmetry and Integration: maa.org/sites/default/files/pdf/mathdl/CMJ/Nelsen39-41.pdf
Jan
7
comment Why can't we model periodic phenomena using a single autonomous differential equation?
Probably it means an equation of the form $x'=f(x)$, since a second-order ODE can of course have periodic solutions. Here's a hint: What does the phase portrait of such a first-order ODE look like? Can solutions return to where they started from?
Jan
3
awarded  Enlightened
Jan
2
revised Where can I find free text to learn Lie group analysis for solving nonlinear systems of differential equations?
edited tags