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Apr
18
reviewed Approve suggested edit on poincare-bendixson theorem contradiction
Apr
18
answered Solid of revolution vs $\iiint$
Apr
18
comment How to find $\nabla$ in spherical coordinates
I'd have thought that $x=r\sin \theta \cos\phi, y= r \sin \theta \sin \phi, z=r \cos \theta$ and the chain rule for partial derivatives is enough (though messy).
Apr
18
answered fourier series, parsevel's identity
Apr
17
awarded  Organizer
Apr
17
revised Solving integral $ \int \frac{x+\sqrt{1+x+x^2}}{1+x+\sqrt{1+x+x^2}}\:\mathrm{d}x $
It's really nothing to do with irrationals.
Apr
17
suggested suggested edit on Solving integral $ \int \frac{x+\sqrt{1+x+x^2}}{1+x+\sqrt{1+x+x^2}}\:\mathrm{d}x $
Apr
17
comment Integral $I=\int_0^\infty \frac{x^4}{(\alpha+x^2)^4}dx$
@Integrals Substitute $t=u^2$, and use $$B(x,y)=\int_0^\infty \frac{t^{x-1}}{(1+t)^{x+y}}dx,$$ where $B(x,y)= \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)}$ is the beta function.
Apr
17
awarded  Talkative
Apr
17
comment How to convert a integral into the another?
@Victor An excellent explanation is here.
Apr
17
comment Closed form for $\int_0^1 \frac{x^a dx}{(1+x^b)^c}$.
This is essentially what the other answers do, the equivalence between their forms and your idea basically comes from the definition of the hypergeometric function.
Apr
17
comment Which $n$th order differential equations have $n$ linearly independent solutions?
Thanks. However, you seem to have just proven the case for $n=2$, not general $n$ (or, indeed, for other types of differential equation).
Apr
17
comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
@AlexB. I've encountered a few things that need $p$-adic numbers, but never a particularly good introduction on them. I know this is not really to do with the original question, but do you know of a good introduction? Regardless, thanks for the speedy response.
Apr
17
comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
@AlexB. What theory is necessary to understand Tate's proof?
Apr
16
revised A question on convergence of Fourier series and the derivative of the function
Fixed LaTeX
Apr
16
suggested suggested edit on A question on convergence of Fourier series and the derivative of the function
Apr
16
revised Integral $I=\int_0^1\frac{\ln x}{x^n-1}dx$
added 504 characters in body
Apr
16
answered Integrate $\displaystyle \int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
Apr
16
comment Integral $I=\int_0^1\frac{\ln x}{x^n-1}dx$
@RandomVariable Oh, and only take the limit after differentiating?
Apr
16
comment Integral $I=\int_0^1\frac{\ln x}{x^n-1}dx$
@RandomVariable Is there a rigorous way one could justify that that would make the integral converge (I'm really bad with this, despite trying to learn some analysis)?