Question

Does there exist a branch of $(a^2 - z^2)^{1/2}$ holomorphic on $\mathbb{C}\setminus [-a,a]$?

score 88 · Answer 1 · 2026-03-24 22:01:43

88

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Does there exist a branch of $(a^2 - z^2)^{1/2}$ holomorphic on $\mathbb{C}\setminus [-a,a]$?

Published on 24 Mar 2026 - 22:01

score 344 · Answer 2 · 2026-03-27 16:55:10

344

Views

Complex Contour Integral Evaluation: $\int_{-\infty}^{\infty} \frac{\cos x-1}{x^2(x^2+4)}dx$

Published on 27 Mar 2026 - 16:55

score 121 · Answer 3 · 2026-03-27 10:15:58

121

Views

Please compute $\int_0^{\infty}e^{-(x+ai)^2}dx$, where, $i^2=-1$.

Published on 27 Mar 2026 - 10:15

score 58 · Answer 4 · 2026-03-27 12:20:07

58

Views

Change of variables integration for all real p>1?

Published on 27 Mar 2026 - 12:20

score 28 · Answer 5 · 2026-03-27 13:40:06

28

Views

Converse of ML inequality for contour integrals

Published on 27 Mar 2026 - 13:40

score 61 · Answer 6 · 2026-03-25 07:41:46

61

Views

Using the Cauchy Principal Value along a differentiable contour?

Published on 25 Mar 2026 - 7:41

score 1k · Answer 7 · 2026-03-27 15:18:18

1k

Views

Taking Residues of Infinity of Square Roots.

Published on 27 Mar 2026 - 15:18

score 149 · Answer 8 · 2026-03-25 19:07:08

149

Views

Proving $g'(z)=\frac{1}{2\pi{}i}\int_{C}\frac{g(u)du}{(u-z)^2}$ for $g(z)$ holomorphic in and on contour $C$, and $z$ in $C$'s interior

Published on 25 Mar 2026 - 19:07

score 50 · Answer 9 · 2026-03-25 00:07:40

50

Views

Branch cut of $\int_0^{\infty} \frac{x^{s-1}}{1+x}$

Published on 25 Mar 2026 - 0:07

score 92 · Answer 10 · 2026-03-29 06:55:41

92

Views

Sign convention for Fourier transform and contour integration - example

Published on 29 Mar 2026 - 6:55

score 64 · Answer 11 · 2019-03-23 10:38:58

64

Views

Using the Cauchy-Goursat theorem to prove a statement

Published on 23 Mar 2019 - 10:38

score 39 · Answer 12 · 2019-03-23 21:01:56

39

Views

Using Contour Integration to solve an integral that holds for all p.

Published on 23 Mar 2019 - 21:01

score 84 · Answer 13 · 2026-03-27 15:17:51

84

Views

Applying the residue theorem to $\log^2(|1+hz|)$

Published on 27 Mar 2026 - 15:17

score 159 · Answer 14 · 2026-03-25 03:19:42

159

Views

Szegő's method of finding the generating function of the Jacobi polynomials

Published on 25 Mar 2026 - 3:19

score 63 · Answer 15 · 2026-03-27 15:19:13

63

Views

Compute the integral $ \int_{Re(s)=2}\frac{x^{-s}}{s^3}ds\quad\text{for real}\ x>0. $

Published on 27 Mar 2026 - 15:19

List Question

Does there exist a branch of $(a^2 - z^2)^{1/2}$ holomorphic on $\mathbb{C}\setminus [-a,a]$?

Complex Contour Integral Evaluation: $\int_{-\infty}^{\infty} \frac{\cos x-1}{x^2(x^2+4)}dx$

Please compute $\int_0^{\infty}e^{-(x+ai)^2}dx$, where, $i^2=-1$.

Change of variables integration for all real p>1?

Converse of ML inequality for contour integrals

Using the Cauchy Principal Value along a differentiable contour?

Taking Residues of Infinity of Square Roots.

Proving $g'(z)=\frac{1}{2\pi{}i}\int_{C}\frac{g(u)du}{(u-z)^2}$ for $g(z)$ holomorphic in and on contour $C$, and $z$ in $C$'s interior

Branch cut of $\int_0^{\infty} \frac{x^{s-1}}{1+x}$

Sign convention for Fourier transform and contour integration - example

Using the Cauchy-Goursat theorem to prove a statement

Using Contour Integration to solve an integral that holds for all p.

Applying the residue theorem to $\log^2(|1+hz|)$

Szegő's method of finding the generating function of the Jacobi polynomials

Compute the integral $ \int_{Re(s)=2}\frac{x^{-s}}{s^3}ds\quad\text{for real}\ x>0. $

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