Question

Show that $\int_{-\infty}^{\infty}\exp\left({-\left(\sqrt {4\pi^{2} t}\xi+\frac{i(y-x)}{2\sqrt t}~\right)^{2}}\right)\,d\xi =\frac{1}{\sqrt {4\pi t}}$

score 94 · Answer 1 · 2026-03-27 23:23:29

94

Views

Show that $\int_{-\infty}^{\infty}\exp\left({-\left(\sqrt {4\pi^{2} t}\xi+\frac{i(y-x)}{2\sqrt t}~\right)^{2}}\right)\,d\xi =\frac{1}{\sqrt {4\pi t}}$

Published on 27 Mar 2026 - 23:23

score 58 · Answer 2 · 2026-03-25 08:08:59

58

Views

prove $\int_{-C}\vec{F}d\vec{R}=-\int_{C} \vec{F}d\vec{R}$

Published on 25 Mar 2026 - 8:08

score 103 · Answer 3 · 2018-03-06 23:43:28

103

Views

Determine all possible values on $\int_{\gamma} \frac{z^3}{(z+3)(z-5)^2} dz$

Published on 06 Mar 2018 - 23:43

score 2.9k · Answer 4 · 2026-03-26 08:03:37

2.9k

Views

Evaluate using contour integration $\int_0^{\pi}\frac{\sin(2\theta)}{5-3\cos(\theta)}d\theta$

Published on 26 Mar 2026 - 8:03

score 2.3k · Answer 5 · 2018-03-07 07:44:57

2.3k

Views

Keyhole contour integration of $\int_0^{\infty}\frac{z^{1/2}\log(z)}{(1+z)^2}dz$

Published on 07 Mar 2018 - 7:44

score 1.2k · Answer 6 · 2026-03-22 20:38:31

1.2k

Views

Does a branch cut discontinuity determine a function near the branch point?

Published on 22 Mar 2026 - 20:38

score 69 · Answer 7 · 2018-03-11 06:43:06

69

Views

What is $\int_0^\infty \frac{\sin(x^2)}{x^2}\ \,dx$?

Published on 11 Mar 2018 - 6:43

score 93 · Answer 8 · 2026-03-25 10:58:59

93

Views

Contour integral of $f(z)$ where $f(z)$ is not defined on the contour.

Published on 25 Mar 2026 - 10:58

score 228 · Answer 9 · 2026-03-25 13:53:40

228

Views

Contour integration along a broken line giving different answer when compared with non broken line

Published on 25 Mar 2026 - 13:53

score 316 · Answer 10 · 2026-03-27 08:31:43

316

Views

Loop contour integration around branch points?

Published on 27 Mar 2026 - 8:31

score 86 · Answer 11 · 2026-03-26 14:29:28

86

Views

Integrating $\frac {x^a\log x}{x^b+1}$ using contour integration

Published on 26 Mar 2026 - 14:29

score 750 · Answer 12 · 2026-03-27 12:47:41

750

Views

Complex Analysis Argument Principle Problem

Published on 27 Mar 2026 - 12:47

score 150 · Answer 13 · 2026-03-20 06:03:14

150

Views

Integral on semicircular arc of a function with a simple pole at $z=0$

Published on 20 Mar 2026 - 6:03

score 375 · Answer 14 · 2026-03-25 13:57:06

375

Views

Compute the integral of $ z^2+ z z*$ where $C=\{ z | |z|=1, 0<argz<\pi \}$

Published on 25 Mar 2026 - 13:57

score 38 · Answer 15 · 2018-03-26 10:46:23

38

Views

Weird result on the evaluation of a Fourier coefficient

Published on 26 Mar 2018 - 10:46

List Question

Show that $\int_{-\infty}^{\infty}\exp\left({-\left(\sqrt {4\pi^{2} t}\xi+\frac{i(y-x)}{2\sqrt t}~\right)^{2}}\right)\,d\xi =\frac{1}{\sqrt {4\pi t}}$

prove $\int_{-C}\vec{F}d\vec{R}=-\int_{C} \vec{F}d\vec{R}$

Determine all possible values on $\int_{\gamma} \frac{z^3}{(z+3)(z-5)^2} dz$

Evaluate using contour integration $\int_0^{\pi}\frac{\sin(2\theta)}{5-3\cos(\theta)}d\theta$

Keyhole contour integration of $\int_0^{\infty}\frac{z^{1/2}\log(z)}{(1+z)^2}dz$

Does a branch cut discontinuity determine a function near the branch point?

What is $\int_0^\infty \frac{\sin(x^2)}{x^2}\ \,dx$?

Contour integral of $f(z)$ where $f(z)$ is not defined on the contour.

Contour integration along a broken line giving different answer when compared with non broken line

Loop contour integration around branch points?

Integrating $\frac {x^a\log x}{x^b+1}$ using contour integration

Complex Analysis Argument Principle Problem

Integral on semicircular arc of a function with a simple pole at $z=0$

Compute the integral of $ z^2+ z z*$ where $C=\{ z | |z|=1, 0<argz<\pi \}$

Weird result on the evaluation of a Fourier coefficient

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