All Questions

I have $f(t)=\dfrac{e^{-i\sqrt{(t-t_0)^2+A^2}}}{\sqrt{(t-t_0)^2+A^2}}$ where $t_0$ and $A$ are constant. I need to take the Fourier transform of $f(t)$. I made few substitutions to take it to a form ...

I have questions about the proof of Theorem $2.1$ here. The proof is on Pg. $10$. I am trying to work out the $d = 2$ case in particular. $$\mathcal C^d = \{(x_1, \ldots, x_{d+1}): |(x_1, \ldots, x_d)|...

I have to work out the integral: $$ \int_0^{\infty} dq \frac{J_0(q \xi)}{q+1} $$ where $ J_0(z) $ is the Bessel function of the first type and order zero, $\xi \in \mathbb{R}$, $\xi \ge 0 $. So far, ...

I am trying to find the inverse of the following kernel in 3 dimensions $$ \nabla^2-x^2, $$ where, $$ x^2=\vec{x}.\vec{x} $$ It seems quit simple and one would think there should already be solutions ...

How can we prove that the Fourier transform of the function $$ f(x) = \begin{cases} (a^2-x^2)^{c/2} BesselJ[c,b\sqrt{a^2-x^2}] & \text{for }x^2 < a^2\\ 0 & \text{otherwise} \end{cases} $$ ...