If $\hat{g}(\omega)=e^{-4 a\pi^2 \omega^2 t}$ then how I show $g=\dfrac{1}{4\pi \sqrt{a\pi t}}\exp\Big(\frac{-x^2}{16a\pi^2 t}\Big)$?
69913
Inverse Fourier transform of Gaussian
134510
How do you get $\rm{var}(\Theta -\hat\theta) = \rm{var}(\Theta)$?
30637
Exponent of $GL(n,q)$.
114411
Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$
109295
Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$
29389
Why does $k/m=\omega^2$ for harmonic motion?
12158
Show that $\arctan\frac{1}{2}+\arctan\frac{1}{3}=\frac{\pi}{4}$
129605
$ 2g(z)=g(\frac{z}{2}) + g(\frac{z+1}{2})$
100711
$\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$
41191
How to prove this $\pi$ formula?
117383
What is the value of $\Gamma(\mathrm{i})$ ?
24416
What is the cleverest way to calculate $[\hat{a}^{M},\hat{a}^{\dagger N}]$ when $[\hat{a},\hat{a}^{\dagger}]=1$?
113080
Prove $\tan\big(\frac{\pi}{2} -\theta \big) = \cot \theta$
104828
Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}...\cot \frac{(m-1)\pi}{2m}=1$
25498
Prove that $\omega + \omega_1 = \omega \cdot \omega_1 = \omega^{\omega_1} = \omega_1$
67489
How to show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?
105177
Gosper's unusual formula connecting $e$ and $\pi$