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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 a Fourier integral $$\int\limits_{-\infty}^{\infty}\mathrm{d}t\,\frac{1}{t^2}\exp\left({\mathrm{i}\frac{t^3}{3}+\mathrm{i}Yt+\frac{\mathrm{i}\lambda^2}{4t}}\right),$$ where $Y$ and $\lambda$ ...

I would like compute the following $$I_{t,x,y} = \int_{\mathbb S^2} e^{-i\left<t,\omega\right>} \, e^{-i\left< A(\omega)x,y\right>} \, d\sigma(\omega); $$ where $\mathbb S^2$ is the two-...