List questions from fresnel-integrals

Published on 23 Feb 2026 - 7:13

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Fresnel integral: stationary phase approx.

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

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Contour integration mistake: Fresnel Integral computes to zero

Published on 23 Feb 2026 - 7:24

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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 23 Feb 2026 - 7:25

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integral from fresnel integral

Published on 23 Feb 2026 - 7:17

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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 23 Feb 2026 - 7:23

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asymptotic approximation of Fresnel integrals with complex argument

Published on 23 Feb 2026 - 7:24

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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 23 Feb 2026 - 7:23

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Quadratic-trigonometric integral -- part 2

Published on 23 Feb 2026 - 7:25

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How to show positivity of Fresnel C integral?

Published on 09 Apr 2026 - 1:39

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Quadratic-trigonometric integral -- part 3

Published on 23 Feb 2026 - 7:25

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Quadratic-trigonometric integral -- part 4

Published on 23 Feb 2026 - 7:17

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

Published on 23 Feb 2026 - 7:20

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Fresnel Integral Proof (without rigorous complex analysis)

Published on 08 Apr 2026 - 14:50

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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