Question

Concluding the solutions of two complex integrals from one.

score 137 · Answer 1 · 2022-01-09 12:14:04

137

Views

Concluding the solutions of two complex integrals from one.

Published on 09 Jan 2022 - 12:14

score 109 · Answer 2 · 2026-03-27 05:39:05

109

Views

Deducing $\int_0^{\pi}\log \sin x dx =-\pi\log 2$ from $\int_0^{\pi}\log (-2ie^{ix}\sin x) dx = 0$

Published on 27 Mar 2026 - 5:39

score 152 · Answer 3 · 2022-01-10 08:30:31

152

Views

Evaluating integrals of the form $\int_{-\infty}^{\infty}R(x)\sin(x)dx$

Published on 10 Jan 2022 - 8:30

score 52 · Answer 4 · 2022-01-10 11:48:30

52

Views

Calculating a modified version of integral representation of the Hankel's function of the first kind

Published on 10 Jan 2022 - 11:48

score 439 · Answer 5 · 2026-03-30 01:48:03

439

Views

Ahlfors page 123: Compute $\int_{|z|=2}z^n(1-z)^mdz$. What happens when $n,m<0$? Residue Theory? Cauchy's Theorem?

Published on 30 Mar 2026 - 1:48

score 164 · Answer 6 · 2022-01-12 16:20:13

164

Views

Show that $\lim_{R \to \infty} \int_0^\pi e^{-R \, \sin(t)}dt = 0$

Published on 12 Jan 2022 - 16:20

score 111 · Answer 7 · 2026-04-09 10:42:09

111

Views

Continuous Positive Function

Published on 09 Apr 2026 - 10:42

score 484 · Answer 8 · 2022-01-14 10:40:22

484

Views

Compute $\int_0^{2\pi} \frac{dx}{3-2\cos x + \sin x}$

Published on 14 Jan 2022 - 10:40

score 267 · Answer 9 · 2022-01-14 20:39:50

267

Views

Compute $\int_{-\infty}^{+\infty} \frac{cos(px)-cos(qx)}{x^2+\epsilon^2}dx$ where $\epsilon,p,q>0$

Published on 14 Jan 2022 - 20:39

score 81 · Answer 10 · 2022-01-18 04:33:06

81

Views

Evaluating the integral $\int_{-\infty}^{\infty} \frac{\sin(x)}{x(x^2+1)}dx$

Published on 18 Jan 2022 - 4:33

score 105 · Answer 11 · 2026-04-09 11:41:56

105

Views

Quadratic-trigonometric integral -- part 2

Published on 09 Apr 2026 - 11:41

score 75 · Answer 12 · 2022-01-20 21:27:50

75

Views

Let $f$ be an entire function such that $f(0)=0$. If $\displaystyle\lim_{|z|\to+\infty}v(z)=0,$ then $f\equiv 0$?

Published on 20 Jan 2022 - 21:27

score 69 · Answer 13 · 2022-01-24 20:59:02

69

Views

For which values of $p \in \mathbb{R} $ is the integral $I = \int_{0}^{\infty} \frac{x^p}{x^2+a^2}dx$ convergent?

Published on 24 Jan 2022 - 20:59

score 173 · Answer 14 · 2022-01-25 04:45:47

173

Views

Solve this integral by hypergeometric function

Published on 25 Jan 2022 - 4:45

score 118 · Answer 15 · 2022-01-26 14:24:05

118

Views

Residue computation for Hirzebruch-Riemann-Roch

Published on 26 Jan 2022 - 14:24

List Question

Concluding the solutions of two complex integrals from one.

Deducing $\int_0^{\pi}\log \sin x dx =-\pi\log 2$ from $\int_0^{\pi}\log (-2ie^{ix}\sin x) dx = 0$

Evaluating integrals of the form $\int_{-\infty}^{\infty}R(x)\sin(x)dx$

Calculating a modified version of integral representation of the Hankel's function of the first kind

Ahlfors page 123: Compute $\int_{|z|=2}z^n(1-z)^mdz$. What happens when $n,m<0$? Residue Theory? Cauchy's Theorem?

Show that $\lim_{R \to \infty} \int_0^\pi e^{-R \, \sin(t)}dt = 0$

Continuous Positive Function

Compute $\int_0^{2\pi} \frac{dx}{3-2\cos x + \sin x}$

Compute $\int_{-\infty}^{+\infty} \frac{cos(px)-cos(qx)}{x^2+\epsilon^2}dx$ where $\epsilon,p,q>0$

Evaluating the integral $\int_{-\infty}^{\infty} \frac{\sin(x)}{x(x^2+1)}dx$

Quadratic-trigonometric integral -- part 2

Let $f$ be an entire function such that $f(0)=0$. If $\displaystyle\lim_{|z|\to+\infty}v(z)=0,$ then $f\equiv 0$?

For which values of $p \in \mathbb{R} $ is the integral $I = \int_{0}^{\infty} \frac{x^p}{x^2+a^2}dx$ convergent?

Solve this integral by hypergeometric function

Residue computation for Hirzebruch-Riemann-Roch

Trending Questions

Popular # Hahtags

Popular Questions