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20m
comment How to prove that $L_2[0,\infty)$ space is linearly isomorphic to $\mathcal{H}_2$ the space of analytic in $Re(s)>0$ functions?
en.wikipedia.org/wiki/Paley%E2%80%93Wiener_theorem
31m
comment use parseval's identity to evaluate the integral $ \int_{-\pi}^{\pi}\sin^4 xdx$
@Cortizol: yes, sure, $\frac{\pi}{2}+\frac{\pi}{4}=\frac{3\pi}{4}$, my bad.
31m
revised use parseval's identity to evaluate the integral $ \int_{-\pi}^{\pi}\sin^4 xdx$
edited body
33m
answered Homework 8th grader: $\pi^2$ is irrational
48m
comment use parseval's identity to evaluate the integral $ \int_{-\pi}^{\pi}\sin^4 xdx$
@user155971: the first line gives the Fourier coefficients of $\sin^2(x)$. The second line is the application of Parseval's identity.
52m
comment use parseval's identity to evaluate the integral $ \int_{-\pi}^{\pi}\sin^4 xdx$
This is true for sure, but where is the application of Parseval's theorem?
53m
answered use parseval's identity to evaluate the integral $ \int_{-\pi}^{\pi}\sin^4 xdx$
3h
answered Estimate from below $\int_0^\pi e^{-t}\cos nt dt$ without calculate it.
3h
answered how to parameterize the ellipse $x^2 + xy + 3y^2 = 1$ with $\sin \theta$ and $\cos \theta$
4h
answered Calculate $\int_{0}^{1} \frac{x^3}{\sqrt{1+x^4}}dx$
4h
answered Integrating $\sin^3(x)/(2+\cos(x))$
5h
comment Solving integral with spherical bessel functions
How do you define $J_{\frac{1}{2}}(z)$ when $z<0$?
7h
comment Solving integral with spherical bessel functions
Really strange. One might guess that $J_{0.5}(z)$ is the Bessel function of the first kind of order one half, also known as: $$J_{\frac{1}{2}}(z)=\sqrt{\frac{2}{\pi z}}\sin(z).$$ Do our notations agree?
7h
comment How to solve the equations of the type $\sin a + \sin b = \sin x$?
Aren't you satisfied by $x=\arcsin(\sin 20+\sin 40)$? Notice that there are trivial issues if the LHS is greater than one or less than minus one.
7h
comment what is the value of $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$?
(+1) Exactly. Equality of $a,b,c$ can also be derived from Newton's inequalities. It is important to notice that $a+b+c$ and $ab+ac+bc$ are symmetric polynomials while $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$ is not a symmetric function.
7h
answered If $X$ has a Poisson distribution with $E[X]=\lambda$, does $Var[X^2]=4\lambda^3+6\lambda^2+\lambda$?
9h
comment integrate $\int \frac{1}{e^{x}+e^{ax}+e^{a^{2}x}} \, dx$
$$\frac{1}{e^x +2e^{-x/2}\cos\frac{x\sqrt{3}}{2}}$$ does not look to have a nice primitive, but maybe the integral over $\mathbb{R}^+$ is more good-looking.
12h
comment Cauchy-Ramanujan Formula $ \displaystyle \sum_{\stackrel{m \in \mathbb{Z}}{m \neq 0}} \frac{\coth m \pi}{m^{4p+3}} $
(+1) Beautiful piece.
22h
comment Prove a $\pi$ inequality: $\left(1+\frac1\pi\right)^{\pi+1}<\pi$
@mjqxxxx: yes, you're right.
1d
answered Average distance from center of circle to evenly-distributed points within it