Question

Contour integral of $e^z / (z-1)^n$.

score 2.9k · Answer 1 · 2026-03-27 08:58:56

2.9k

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Contour integral of $e^z / (z-1)^n$.

Published on 27 Mar 2026 - 8:58

score 141 · Answer 2 · 2026-04-04 03:02:18

141

Views

Showing contour integral $\int_{C_R}\frac{e^{st}}{\sqrt{s}}\,ds$ goes to $0$

Published on 04 Apr 2026 - 3:02

score 135 · Answer 3 · 2026-04-04 03:03:24

135

Views

Calculating Inverse Laplace Transform of ((1+s/wh)/(1+s/wb))^n

Published on 04 Apr 2026 - 3:03

score 481 · Answer 4 · 2026-03-26 06:31:02

481

Views

Hyperbolic sums $S(n,k)=\sum_{m=1}^{\infty} \frac{1}{\cosh(\pi m)^{n} \sinh(\pi m)^{k}}$

Published on 26 Mar 2026 - 6:31

score 43 · Answer 5 · 2026-04-01 11:15:29

43

Views

Gauss' formula on positively oriented closed contour

Published on 01 Apr 2026 - 11:15

score 164 · Answer 6 · 2026-04-01 11:21:18

164

Views

Evaluation of the infinite series $\sum_{n=1}^\infty (-1)^{n-1} \frac{\overline{H}_n}{n \binom{2n}{n}}$

Published on 01 Apr 2026 - 11:21

score 19 · Answer 7 · 2023-02-02 23:27:58

19

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Analytic continuation of $\int_{-\infty + i \cdot p}^{\infty + i \cdot p} \exp\left[ -w^{2} +\left|w-y- i\cdot p\right|-y^{2}\right]\operatorname{d}w$

Published on 02 Feb 2023 - 23:27

score 62 · Answer 8 · 2023-02-05 14:49:11

62

Views

How to set up the contour for $ \int_{-\infty}^{+\infty} \frac{e^{iax}}{1+x^4}dx $?

Published on 05 Feb 2023 - 14:49

score 281 · Answer 9 · 2023-02-06 07:30:15

281

Views

Evaluating $\int_{-\infty}^{\infty}\frac{\ln\left(1+x^{8}\right)}{x^{2}\left(1+x^{2}\right)^{2}}dx$

Published on 06 Feb 2023 - 7:30

score 584 · Answer 10 · 2026-03-31 10:34:52

584

Views

A dodgy contour integration method giving the correct result

Published on 31 Mar 2026 - 10:34

score 265 · Answer 11 · 2023-02-13 22:53:00

265

Views

An attempt at generalizing a family of integrals $\int_0^{\alpha}{\frac{\sin \left( \pi x \right)}{x^x\left( \alpha -x \right) ^{\alpha -x}}}\, dx$

Published on 13 Feb 2023 - 22:53

score 59 · Answer 12 · 2026-03-25 15:47:20

59

Views

Growth rate of Mellin transform

Published on 25 Mar 2026 - 15:47

score 68 · Answer 13 · 2026-03-29 18:51:05

68

Views

Hints to solve an equation containing $\int\frac{dx}{x\sqrt{(1+x^{-4})^n-1}}$ for $n<0$

Published on 29 Mar 2026 - 18:51

score 103 · Answer 14 · 2026-04-04 04:28:15

103

Views

Solving $\frac{d^2u}{dt^2} + u = e^{-t}\cos{t}$ using the Laplace Transform

Published on 04 Apr 2026 - 4:28

score 91 · Answer 15 · 2026-03-29 18:53:40

91

Views

Strategy for integrating product of powers and trigonometric functions

Published on 29 Mar 2026 - 18:53

List Question

Contour integral of $e^z / (z-1)^n$.

Showing contour integral $\int_{C_R}\frac{e^{st}}{\sqrt{s}}\,ds$ goes to $0$

Calculating Inverse Laplace Transform of ((1+s/wh)/(1+s/wb))^n

Hyperbolic sums $S(n,k)=\sum_{m=1}^{\infty} \frac{1}{\cosh(\pi m)^{n} \sinh(\pi m)^{k}}$

Gauss' formula on positively oriented closed contour

Evaluation of the infinite series $\sum_{n=1}^\infty (-1)^{n-1} \frac{\overline{H}_n}{n \binom{2n}{n}}$

Analytic continuation of $\int_{-\infty + i \cdot p}^{\infty + i \cdot p} \exp\left[ -w^{2} +\left|w-y- i\cdot p\right|-y^{2}\right]\operatorname{d}w$

How to set up the contour for $ \int_{-\infty}^{+\infty} \frac{e^{iax}}{1+x^4}dx $?

Evaluating $\int_{-\infty}^{\infty}\frac{\ln\left(1+x^{8}\right)}{x^{2}\left(1+x^{2}\right)^{2}}dx$

A dodgy contour integration method giving the correct result

An attempt at generalizing a family of integrals $\int_0^{\alpha}{\frac{\sin \left( \pi x \right)}{x^x\left( \alpha -x \right) ^{\alpha -x}}}\, dx$

Growth rate of Mellin transform

Hints to solve an equation containing $\int\frac{dx}{x\sqrt{(1+x^{-4})^n-1}}$ for $n<0$

Solving $\frac{d^2u}{dt^2} + u = e^{-t}\cos{t}$ using the Laplace Transform

Strategy for integrating product of powers and trigonometric functions

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