Question

How can I calculate $\int_{-\infty}^{\infty}e^{-x^2+ix}dx$?

score 62 · Answer 1 · 2026-04-04 06:04:41

62

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How can I calculate $\int_{-\infty}^{\infty}e^{-x^2+ix}dx$?

Published on 04 Apr 2026 - 6:04

score 227 · Answer 2 · 2026-02-23 10:49:50

227

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The direction of the steepest descent path at the saddle point (Picard-Lefschetz theory)

Published on 23 Feb 2026 - 10:49

score 187 · Answer 3 · 2021-11-24 14:48:17

187

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How to find $\int_{0}^{2\pi} \frac{\cos(n\theta)}{(\cos(\theta)+\alpha)^2}d\theta, \alpha>1$

Published on 24 Nov 2021 - 14:48

score 675 · Answer 4 · 2021-11-26 13:38:30

675

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Why am I getting 2 different answers for Integral exp(ix) from 0 to Infinity

Published on 26 Nov 2021 - 13:38

score 108 · Answer 5 · 2021-11-27 04:56:52

108

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"Dog bone" integral when computing $\int_{-1}^{1} \mathop{\mathrm{d}x} \frac{(1-x)^{-2/3}(1+x)^{-1/3}}{4+x^2}$

Published on 27 Nov 2021 - 4:56

score 60 · Answer 6 · 2026-03-30 00:05:37

60

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Solve $\int _{|z-1|=1} \frac{\log{z}}{z^{4}} dz $

Published on 30 Mar 2026 - 0:05

score 26 · Answer 7 · 2026-03-29 20:17:36

26

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Given $|\int f(\zeta)\,d\zeta-1|<\epsilon$, what can we say about $\int|f(\zeta)|\,d|\zeta|$?

Published on 29 Mar 2026 - 20:17

score 26 · Answer 8 · 2026-03-29 20:14:54

26

Views

Integrating the gaussian kernel on unbounded curves in $\Bbb C$

Published on 29 Mar 2026 - 20:14

score 782 · Answer 9 · 2026-03-29 23:58:47

782

Views

Complex integration: $ \int_{c} \frac{e^{z}}{z(z-3)} dz$

Published on 29 Mar 2026 - 23:58

score 127 · Answer 10 · 2026-03-28 03:55:29

127

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$f$ analytic in $\overline{\mathbb{D}}$ s.t $\int_{|z|=1}|f(z)-z||dz|\leq\frac{1}{100}$. Prove that $f$ has at least one zero in $\mathbb{D}$.

Published on 28 Mar 2026 - 3:55

score 65 · Answer 11 · 2026-03-31 19:45:15

65

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$\int_C|f_n(z)||dz|\leq M$ for each $f_n$. Prove $\{f_n\}$ has a subsequence converging uniformly on compact subsets of $D$.

Published on 31 Mar 2026 - 19:45

score 99 · Answer 12 · 2021-12-07 17:28:03

99

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Evaluate $\int_0^{2\pi} \frac{\cos x}{2x^2 + 1} \,\mathrm{d}x$ using complex analysis

Published on 07 Dec 2021 - 17:28

score 108 · Answer 13 · 2021-12-08 06:36:23

108

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if f is integer and satisfies $| f (z) | ≤ | z |^n$ then f must be a polynomial

Published on 08 Dec 2021 - 6:36

score 522 · Answer 14 · 2026-03-27 07:18:44

522

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Show that $ \int_{-1}^{1} z^{i} dz= \frac{1 + e^{- \pi}}{2} (1 -i)$

Published on 27 Mar 2026 - 7:18

score 77 · Answer 15 · 2021-12-08 18:10:52

77

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Evaluate $\int_{-\infty}^{0} \frac{x}{x^3-1} \, \mathrm{d}x$ by using complex analysis

Published on 08 Dec 2021 - 18:10

List Question

How can I calculate $\int_{-\infty}^{\infty}e^{-x^2+ix}dx$?

The direction of the steepest descent path at the saddle point (Picard-Lefschetz theory)

How to find $\int_{0}^{2\pi} \frac{\cos(n\theta)}{(\cos(\theta)+\alpha)^2}d\theta, \alpha>1$

Why am I getting 2 different answers for Integral exp(ix) from 0 to Infinity

"Dog bone" integral when computing $\int_{-1}^{1} \mathop{\mathrm{d}x} \frac{(1-x)^{-2/3}(1+x)^{-1/3}}{4+x^2}$

Solve $\int _{|z-1|=1} \frac{\log{z}}{z^{4}} dz $

Given $|\int f(\zeta)\,d\zeta-1|<\epsilon$, what can we say about $\int|f(\zeta)|\,d|\zeta|$?

Integrating the gaussian kernel on unbounded curves in $\Bbb C$

Complex integration: $ \int_{c} \frac{e^{z}}{z(z-3)} dz$

$f$ analytic in $\overline{\mathbb{D}}$ s.t $\int_{|z|=1}|f(z)-z||dz|\leq\frac{1}{100}$. Prove that $f$ has at least one zero in $\mathbb{D}$.

$\int_C|f_n(z)||dz|\leq M$ for each $f_n$. Prove $\{f_n\}$ has a subsequence converging uniformly on compact subsets of $D$.

Evaluate $\int_0^{2\pi} \frac{\cos x}{2x^2 + 1} \,\mathrm{d}x$ using complex analysis

if f is integer and satisfies $| f (z) | ≤ | z |^n$ then f must be a polynomial

Show that $ \int_{-1}^{1} z^{i} dz= \frac{1 + e^{- \pi}}{2} (1 -i)$

Evaluate $\int_{-\infty}^{0} \frac{x}{x^3-1} \, \mathrm{d}x$ by using complex analysis

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