List questions from fresnel-integrals

Published on 26 Sep 2020 - 16:55

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Fresnel integral: stationary phase approx.

Published on 23 Dec 2020 - 10:34

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How to prove the positivity of Fresnel-like integrals in the positive real axis

Published on 27 Dec 2020 - 21:07

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Contour integration mistake: Fresnel Integral computes to zero

Published on 06 Apr 2021 - 17:08

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Proof of $\int_{0}^{\infty}\sin(x^2)dx=\int_{0}^{\infty}\cos(x^2)dx=\frac{\sqrt{2\pi}}{4}$

Published on 21 May 2021 - 7:15

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integral from fresnel integral

Published on 20 Aug 2021 - 0:06

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Does this Auxiliary Fresnel Sum=$\frac1{2\sqrt2\pi}\int \limits_0^\infty \frac{\vartheta_3\left(e^{-\frac{\pi x}2}\right)\sqrt x}{x^2+1}dx +\frac14 $?

Published on 12 Oct 2021 - 3:35

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asymptotic approximation of Fresnel integrals with complex argument

Published on 27 Oct 2021 - 12:02

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Closed form of $\int e^{i\csc^2(x)}dx=\int \cos\left(\csc^2(x)\right)dx+i\int \sin\left(\csc^2(x)\right)dx$

Published on 11 Nov 2021 - 23:47

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Quadratic-trigonometric integral -- part 2

Published on 19 Jan 2022 - 19:20

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How to show positivity of Fresnel C integral?

Published on 20 Jan 2022 - 0:46

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Quadratic-trigonometric integral -- part 3

Published on 20 Jan 2022 - 22:47

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Quadratic-trigonometric integral -- part 4

Published on 23 Jan 2022 - 11:01

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Computing $\int_0^t \tau \cos(c+b\tau+a\tau^2)\text{ d}\tau$ -- part 2

Published on 27 Jan 2022 - 19:53

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Fresnel Integral Proof (without rigorous complex analysis)

Published on 01 May 2022 - 5:09

List Question

Fresnel integrals

Fresnel integral: stationary phase approx.

How to prove the positivity of Fresnel-like integrals in the positive real axis

Contour integration mistake: Fresnel Integral computes to zero

Proof of $\int_{0}^{\infty}\sin(x^2)dx=\int_{0}^{\infty}\cos(x^2)dx=\frac{\sqrt{2\pi}}{4}$

integral from fresnel integral

Does this Auxiliary Fresnel Sum=$\frac1{2\sqrt2\pi}\int \limits_0^\infty \frac{\vartheta_3\left(e^{-\frac{\pi x}2}\right)\sqrt x}{x^2+1}dx +\frac14 $?

asymptotic approximation of Fresnel integrals with complex argument

Closed form of $\int e^{i\csc^2(x)}dx=\int \cos\left(\csc^2(x)\right)dx+i\int \sin\left(\csc^2(x)\right)dx$

Quadratic-trigonometric integral -- part 2

How to show positivity of Fresnel C integral?

Quadratic-trigonometric integral -- part 3

Quadratic-trigonometric integral -- part 4

Computing $\int_0^t \tau \cos(c+b\tau+a\tau^2)\text{ d}\tau$ -- part 2

Fresnel Integral Proof (without rigorous complex analysis)

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