Question

Integrating $\sin(x)/x$, how to treat the pole at the origin?

score 2.7k · Answer 1 · 2015-12-20 02:22:06

2.7k

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Integrating $\sin(x)/x$, how to treat the pole at the origin?

Published on 20 Dec 2015 - 2:22

score 111 · Answer 2 · 2015-12-21 11:05:13

111

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If $\lim\inf_{r\to 0}{r}\cdot \max_{|z|=r}|{f(z)}|=0$ then $0$ is removable singularity.

Published on 21 Dec 2015 - 11:05

score 45 · Answer 3 · 2015-12-21 20:21:07

45

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contour integration problem..

Published on 21 Dec 2015 - 20:21

score 308 · Answer 4 · 2026-03-31 10:13:44

308

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How do I get $ \int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$?

Published on 31 Mar 2026 - 10:13

score 60 · Answer 5 · 2015-12-22 15:48:31

60

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Two Indefinite Integrals

Published on 22 Dec 2015 - 15:48

score 638 · Answer 6 · 2015-12-22 16:10:19

638

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How to prove that $\int_0^\infty\frac{\left(x^2+x+\frac{1}{12}\right)e^{-x}}{\left(x^2+x+\frac{3}{4}\right)^3\sqrt{x}}\ dx=\frac{2\sqrt{\pi}}{9}$?

Published on 22 Dec 2015 - 16:10

score 665 · Answer 7 · 2026-03-31 12:48:21

665

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Laurent expansion of $\operatorname{sech}(z)$ centred at $\pi i/2$

Published on 31 Mar 2026 - 12:48

score 1k · Answer 8 · 2015-12-24 02:51:06

1k

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evaluate the path integral around a circle in complex plane

Published on 24 Dec 2015 - 2:51

score 1.4k · Answer 9 · 2015-12-24 17:36:47

1.4k

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Finding Cauchy Principal Value for $\int_0^\infty \frac{\ln^2x }{(1-x)^2\sqrt{x}(x-4)} dx$

Published on 24 Dec 2015 - 17:36

score 598 · Answer 10 · 2026-04-09 11:13:45

598

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Violating Cauchy's Integral Theorem

Published on 09 Apr 2026 - 11:13

score 1.5k · Answer 11 · 2026-03-26 07:44:13

1.5k

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Contour integral with a logarithm squared: $\int_0^\infty \frac{\log^2 x \, dx}{(1+x)^2}$

Published on 26 Mar 2026 - 7:44

score 69 · Answer 12 · 2026-04-07 22:59:22

69

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Express $\int_{\sin nx}^{\sin(n+1)x}\sin t^2dt$ in terms of $x$ and $n$

Published on 07 Apr 2026 - 22:59

score 413 · Answer 13 · 2015-12-29 21:14:29

413

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Computing $\sum\limits_{n=1}^\infty\frac{\sin n}{n}$ with residues

Published on 29 Dec 2015 - 21:14

score 265 · Answer 14 · 2026-04-03 22:01:04

265

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Computing alternating sum using contour integration

Published on 03 Apr 2026 - 22:01

score 74 · Answer 15 · 2015-12-30 14:56:45

74

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how to evaluate this contour integral

Published on 30 Dec 2015 - 14:56

List Question

Integrating $\sin(x)/x$, how to treat the pole at the origin?

If $\lim\inf_{r\to 0}{r}\cdot \max_{|z|=r}|{f(z)}|=0$ then $0$ is removable singularity.

contour integration problem..

How do I get $ \int_0^1 \frac{dz}{\sqrt{z(z - 1\,)(z+1\,)}} = \frac{\sqrt{\pi}}{2} \frac{\Gamma(\frac{3}{4})}{\Gamma(\frac{9}{4})}$?

Two Indefinite Integrals

How to prove that $\int_0^\infty\frac{\left(x^2+x+\frac{1}{12}\right)e^{-x}}{\left(x^2+x+\frac{3}{4}\right)^3\sqrt{x}}\ dx=\frac{2\sqrt{\pi}}{9}$?

Laurent expansion of $\operatorname{sech}(z)$ centred at $\pi i/2$

evaluate the path integral around a circle in complex plane

Finding Cauchy Principal Value for $\int_0^\infty \frac{\ln^2x }{(1-x)^2\sqrt{x}(x-4)} dx$

Violating Cauchy's Integral Theorem

Contour integral with a logarithm squared: $\int_0^\infty \frac{\log^2 x \, dx}{(1+x)^2}$

Express $\int_{\sin nx}^{\sin(n+1)x}\sin t^2dt$ in terms of $x$ and $n$

Computing $\sum\limits_{n=1}^\infty\frac{\sin n}{n}$ with residues

Computing alternating sum using contour integration

how to evaluate this contour integral

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