Question

Evaluating $\int_{-\infty}^0\frac{1-e^{(1+7i)z}}{e^{-z}-1}dz$ as the generalized harmonic number $H_{1+7i}$

score 48 · Answer 1 · 2026-03-28 08:10:00

48

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Evaluating $\int_{-\infty}^0\frac{1-e^{(1+7i)z}}{e^{-z}-1}dz$ as the generalized harmonic number $H_{1+7i}$

Published on 28 Mar 2026 - 8:10

score 300 · Answer 2 · 2026-03-25 13:54:09

300

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Mellin inversion and the entire function $\varphi(s)=\frac{1-e^{2s}}{e^{-s}-1}$

Published on 25 Mar 2026 - 13:54

score 259 · Answer 3 · 2026-03-27 00:05:52

259

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converse cauchy integral's formula: $F$ is holomorphic if $F(w) = \frac{1}{2\pi i} \oint_{\gamma} \frac{F(z)}{z-w} d z$?

Published on 27 Mar 2026 - 0:05

score 335 · Answer 4 · 2026-03-29 14:20:17

335

Views

How to obtain solution to constants "c_n" from Fourier's trick?

Published on 29 Mar 2026 - 14:20

score 95 · Answer 5 · 2026-03-29 17:33:47

95

Views

Evaluating complex integral of Bessel functions

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score 53 · Answer 6 · 2016-09-29 10:59:41

53

Views

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score 86 · Answer 7 · 2016-10-03 13:58:55

86

Views

$\int_{-\pi}^\pi\sin^2x\cos^2x\ dx$ with complex integral theorems

Published on 03 Oct 2016 - 13:58

score 195 · Answer 8 · 2016-10-05 14:26:47

195

Views

Evaluation of integral related to Gamma function

Published on 05 Oct 2016 - 14:26

score 889 · Answer 9 · 2016-10-05 21:17:13

889

Views

Odd and even functions when applying the Residue Theorem

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score 108 · Answer 10 · 2026-03-26 22:19:26

108

Views

Complex Analysis, Contour Integral Formula

Published on 26 Mar 2026 - 22:19

score 167 · Answer 11 · 2016-10-11 19:44:44

167

Views

Help with integration of $\mathrm{exp}(jxt)/(x^2 + a^2)$

Published on 11 Oct 2016 - 19:44

score 510 · Answer 12 · 2026-03-25 14:25:42

510

Views

Evaluating the closed contour integral $\int_\gamma\frac{e^{-\sqrt{z}}}{(z-b)^{k+1}}dz$

Published on 25 Mar 2026 - 14:25

score 99 · Answer 13 · 2016-10-13 21:37:53

99

Views

Prove that $\int^{\pi}_0 \ln \left(\frac{b-\cos x}{a- \cos x}\right)dx=\pi \ln (\frac{b+\sqrt{b^2-1}}{a+\sqrt{a^2-1}})$

Published on 13 Oct 2016 - 21:37

score 148 · Answer 14 · 2016-10-15 21:06:20

148

Views

What is the logic behind the trigonometric substitution method in integration?

Published on 15 Oct 2016 - 21:06

score 30 · Answer 15 · 2016-10-16 04:55:28

30

Views

Evaluate the integrals using parametrizitons of the contours of integration

Published on 16 Oct 2016 - 4:55

List Question

Evaluating $\int_{-\infty}^0\frac{1-e^{(1+7i)z}}{e^{-z}-1}dz$ as the generalized harmonic number $H_{1+7i}$

Mellin inversion and the entire function $\varphi(s)=\frac{1-e^{2s}}{e^{-s}-1}$

converse cauchy integral's formula: $F$ is holomorphic if $F(w) = \frac{1}{2\pi i} \oint_{\gamma} \frac{F(z)}{z-w} d z$?

How to obtain solution to constants "c_n" from Fourier's trick?

Evaluating complex integral of Bessel functions

how to find analytic function?

$\int_{-\pi}^\pi\sin^2x\cos^2x\ dx$ with complex integral theorems

Evaluation of integral related to Gamma function

Odd and even functions when applying the Residue Theorem

Complex Analysis, Contour Integral Formula

Help with integration of $\mathrm{exp}(jxt)/(x^2 + a^2)$

Evaluating the closed contour integral $\int_\gamma\frac{e^{-\sqrt{z}}}{(z-b)^{k+1}}dz$

Prove that $\int^{\pi}_0 \ln \left(\frac{b-\cos x}{a- \cos x}\right)dx=\pi \ln (\frac{b+\sqrt{b^2-1}}{a+\sqrt{a^2-1}})$

What is the logic behind the trigonometric substitution method in integration?

Evaluate the integrals using parametrizitons of the contours of integration

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