Questions on the Fresnel integrals.

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What do you call a frequency that varies by a function?

I have a concept that I need to learn more about, but I don't know what it's called so I'm not sure what search terms to use to look for it. I apologize in advance that while I'm comfortable with ...
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42 views

Uniform convergence of the complex Fresnel integral

Consider the integral $I(\lambda) = \sqrt {\frac {\lambda \mathbb{i}}{\pi}}^n \int_U \mathbb{e}^{-\mathbb{i} \lambda \|x\ - x_0|^2} f(x) \mathbb{d}x, \lambda>0$ and $U$ some open neighbourhood of ...
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169 views

The inverse laplace transform of $p^{-3/2}e^{-\sqrt{pa}}(\cos(\sqrt{ap})+\sin(\sqrt{ap}))$ can be written in Fresnel integrals?

I used the Residue theorem to solve this problem. But, I could not obtain the solution given by $$\mathscr{L}^{-1}\left( { p^{-3/2}e^{-\sqrt{pa}}\over{2\sqrt{2}}} [\cos(\sqrt{ap})+\sin(\sqrt{ap})] ...
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68 views

Compute Erf(z) using Fresnel integrals

I have to compute $\operatorname{erf}(z)$ using the Fresnel integrals. I have the relation: $$C(z)+iS(z)=\frac{1+i}{2}\operatorname{erf}\left[ \frac{\sqrt{\pi}}{2}(1-i)z \right].$$ But ...