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2h
answered How to prove $\frac{2^a+3}{2^a-9}$ is not a natural number
19h
revised $ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
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20h
comment $ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
FYI, there is now (at least) one other post on the identical question with a link to this one: math.stackexchange.com/questions/1376575/…
20h
comment Show that the standard integral: $\int_{0}^{\infty} x^4\mathrm{e}^{-\alpha x^2}\mathrm dx =\frac{3}{8}{(\frac{\pi}{\alpha^5})}^\frac{1}{2}$
The general principle is that the earlier post on the same question has higher status. What I would like to see happen is for this question to be closed--as it would be in any normal circumstance--and for my earlier post to be reopened. I have voted that way; now it is up to the rest of the community and those who actively review such matters.
20h
revised $ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
added 4 characters in body
20h
comment Show that the standard integral: $\int_{0}^{\infty} x^4\mathrm{e}^{-\alpha x^2}\mathrm dx =\frac{3}{8}{(\frac{\pi}{\alpha^5})}^\frac{1}{2}$
I tried to collect a number of methods here: math.stackexchange.com/questions/1149907/…
23h
answered Sine/cosine series
2d
comment Area under bijective decreasing function
Try drawing a single diagram showing the area of both integrals. Now compare with the area of the natural rectangles.
Jul
26
revised Why people use the Gram-Schmidt process instead of just chosing the standard basis
deleted 4 characters in body
Jul
25
reviewed Leave Closed What is elnekiti's triangle? (edited)
Jul
25
comment Max value of Z, maybe Lagrange multipliers?
If you're going to give the answer, at least show us how it is derived.
Jul
25
comment Confusion about the definition of reflexive relation
Understood. I stand corrected.
Jul
25
revised What theorem is this? (in PDE)
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Jul
25
revised What theorem is this? (in PDE)
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Jul
25
revised What theorem is this? (in PDE)
added 211 characters in body
Jul
25
answered What theorem is this? (in PDE)
Jul
24
comment Laplace transform $\mathcal{L}\{ t^{-2}\}$
Does the improper integral $$\int_0^\infty t^{-n} e^{-st} \ dt$$ for positive integer $n$ converge?
Jul
24
comment Confusion about the definition of reflexive relation
So you're arguing that a theorem such as $$n \in \mathbb N \Rightarrow n+1 \in\mathbb N$$ is incomplete and we actually have to write $$\text{ for all } n \in\mathbb N, n \in\mathbb N \Rightarrow n+1 \in\mathbb N$$ This strikes me as a bit much and outside the bounds of usual mathematical writing, but I take your point.
Jul
24
comment Ignoring the workspace in quantum computation
If you have correspondence from him you could post, that would be instructive.
Jul
24
comment Prove that there doesn't exist any integer $x \ge 3$ such that $x^2-1$ is prime.
Have you tried factoring $x^2 - 1$?